| Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (3100 entries) |
| Axiom Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (13 entries) |
| Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (2517 entries) |
| Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (8 entries) |
| Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (10 entries) |
| Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (517 entries) |
| Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (24 entries) |
| Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (11 entries) |
Global Index
A
Axioms [module, in set1]Axioms.arrow_extensionality [lemma, in set1]
Axioms.equal_or_not [lemma, in set1]
Axioms.inc [definition, in set1]
Axioms.inc_or_not [lemma, in set1]
Axioms.nonempty [inductive, in set1]
Axioms.nonemptyT [inductive, in set1]
Axioms.nonemptyT_intro [constructor, in set1]
Axioms.nonempty_intro [constructor, in set1]
Axioms.p_or_not_p [lemma, in set1]
Axioms.sub [definition, in set1]
axiom_of_pair [axiom, in set1]
B
Bfunction [module, in set2]Bfunction.acreate_bijective [lemma, in set2]
Bfunction.acreate_fgraph [lemma, in set2]
Bfunction.acreate_function [lemma, in set2]
Bfunction.acreate_injective [lemma, in set2]
Bfunction.acreate_source [lemma, in set2]
Bfunction.acreate_surjective [lemma, in set2]
Bfunction.acreate_target [lemma, in set2]
Bfunction.acreate_W [lemma, in set2]
Bfunction.agreeC [definition, in set2]
Bfunction.agrees_on [definition, in set2]
Bfunction.agrees_same_restriction [lemma, in set2]
Bfunction.agrees_same_restrictionC [lemma, in set2]
Bfunction.bcreate [definition, in set2]
Bfunction.bcreate1 [definition, in set2]
Bfunction.bcreate1_bijective [lemma, in set2]
Bfunction.bcreate1_injective [lemma, in set2]
Bfunction.bcreate1_surjective [lemma, in set2]
Bfunction.bcreate_bijective [lemma, in set2]
Bfunction.bcreate_eq [lemma, in set2]
Bfunction.bcreate_injective [lemma, in set2]
Bfunction.bcreate_inv1 [lemma, in set2]
Bfunction.bcreate_inv2 [lemma, in set2]
Bfunction.bcreate_inv3 [lemma, in set2]
Bfunction.bcreate_surjective [lemma, in set2]
Bfunction.bijective [definition, in set2]
Bfunction.bijectiveC [definition, in set2]
Bfunction.bijectiveC_pr [lemma, in set2]
Bfunction.bijective_double_inverseC [lemma, in set2]
Bfunction.bijective_double_inverseC1 [lemma, in set2]
Bfunction.bijective_ext_to_prod2C [lemma, in set2]
Bfunction.bijective_from_compose [lemma, in set2]
Bfunction.bijective_inverseC [lemma, in set2]
Bfunction.bijective_inv_aux [lemma, in set2]
Bfunction.bijective_inv_function [lemma, in set2]
Bfunction.bijective_pr [lemma, in set2]
Bfunction.bijective_source_aux [lemma, in set2]
Bfunction.bijective_target_aux [lemma, in set2]
Bfunction.bij_is_function [lemma, in set2]
Bfunction.bij_left_compose [lemma, in set2]
Bfunction.bij_left_inverse [lemma, in set2]
Bfunction.bij_left_inverseC [lemma, in set2]
Bfunction.bij_right_compose [lemma, in set2]
Bfunction.bij_right_inverse [lemma, in set2]
Bfunction.bij_right_inverseC [lemma, in set2]
Bfunction.BL [definition, in set2]
Bfunction.bl_bijective [lemma, in set2]
Bfunction.bl_function [lemma, in set2]
Bfunction.bl_graph1 [lemma, in set2]
Bfunction.bl_graph2 [lemma, in set2]
Bfunction.bl_graph3 [lemma, in set2]
Bfunction.bl_graph4 [lemma, in set2]
Bfunction.bl_injective [lemma, in set2]
Bfunction.bl_recovers [lemma, in set2]
Bfunction.bl_source [lemma, in set2]
Bfunction.bl_surjective [lemma, in set2]
Bfunction.bl_target [lemma, in set2]
Bfunction.bl_W [lemma, in set2]
Bfunction.bourbaki_ex5_17 [lemma, in set2]
Bfunction.canonical_decomposition1 [lemma, in set2]
Bfunction.canonical_decomposition1C [lemma, in set2]
Bfunction.canonical_injection [definition, in set2]
Bfunction.ci_function [lemma, in set2]
Bfunction.ci_injective [lemma, in set2]
Bfunction.ci_range [lemma, in set2]
Bfunction.ci_W [lemma, in set2]
Bfunction.composable [definition, in set2]
Bfunction.composable_acreate [lemma, in set2]
Bfunction.composable_ext_to_prod2 [lemma, in set2]
Bfunction.composable_f_inv [lemma, in set2]
Bfunction.composable_inv_f [lemma, in set2]
Bfunction.composable_pr [lemma, in set2]
Bfunction.composable_pr1 [lemma, in set2]
Bfunction.composeC [definition, in set2]
Bfunction.composeC_bij [lemma, in set2]
Bfunction.composeC_inj [lemma, in set2]
Bfunction.composeC_surj [lemma, in set2]
Bfunction.compose_acreate [lemma, in set2]
Bfunction.compose_assoc [lemma, in set2]
Bfunction.compose_bijective [lemma, in set2]
Bfunction.compose_domain [lemma, in set2]
Bfunction.compose_ext_to_prod2 [lemma, in set2]
Bfunction.compose_ext_to_prod2C [lemma, in set2]
Bfunction.compose_function [lemma, in set2]
Bfunction.compose_id_left [lemma, in set2]
Bfunction.compose_id_leftC [lemma, in set2]
Bfunction.compose_id_right [lemma, in set2]
Bfunction.compose_id_rightC [lemma, in set2]
Bfunction.compose_injective [lemma, in set2]
Bfunction.compose_source [lemma, in set2]
Bfunction.compose_surjective [lemma, in set2]
Bfunction.compose_target [lemma, in set2]
Bfunction.compose_W [lemma, in set2]
Bfunction.compositionC_associative [lemma, in set2]
Bfunction.constant_constant_fun [lemma, in set2]
Bfunction.constant_function [definition, in set2]
Bfunction.constant_functionC [definition, in set2]
Bfunction.constant_function_fun [lemma, in set2]
Bfunction.constant_function_pr [lemma, in set2]
Bfunction.constant_function_prop2 [lemma, in set2]
Bfunction.constant_fun_constantC [lemma, in set2]
Bfunction.constant_fun_pr [lemma, in set2]
Bfunction.constant_fun_prC [lemma, in set2]
Bfunction.constant_graph [lemma, in set2]
Bfunction.constant_source [lemma, in set2]
Bfunction.constant_target [lemma, in set2]
Bfunction.constant_W [lemma, in set2]
Bfunction.corresp_functionT [definition, in set2]
Bfunction.corresp_functionT_prop [lemma, in set2]
Bfunction.defined_lemT [lemma, in set2]
Bfunction.diagonal_application [definition, in set2]
Bfunction.diag_app_function [lemma, in set2]
Bfunction.diag_app_range [lemma, in set2]
Bfunction.diag_app_W [lemma, in set2]
Bfunction.direct_inv_im [lemma, in set2]
Bfunction.direct_inv_im_surjective [lemma, in set2]
Bfunction.domain_IM [lemma, in set2]
Bfunction.empty_function [definition, in set2]
Bfunction.empty_functionC [definition, in set2]
Bfunction.empty_function_function [lemma, in set2]
Bfunction.empty_function_graph [lemma, in set2]
Bfunction.empty_function_prop [lemma, in set2]
Bfunction.equipotent [definition, in set2]
Bfunction.equipotentC [lemma, in set2]
Bfunction.equipotent_prod_singleton [lemma, in set2]
Bfunction.equipotent_reflexive [lemma, in set2]
Bfunction.equipotent_symmetric [lemma, in set2]
Bfunction.equipotent_transitive [lemma, in set2]
Bfunction.exists_left_composable [lemma, in set2]
Bfunction.exists_left_composableC [lemma, in set2]
Bfunction.exists_left_composable_aux [lemma, in set2]
Bfunction.exists_left_composable_auxC [lemma, in set2]
Bfunction.exists_left_inv_from_inj [lemma, in set2]
Bfunction.exists_left_inv_from_injC [lemma, in set2]
Bfunction.exists_right_composable [lemma, in set2]
Bfunction.exists_right_composableC [lemma, in set2]
Bfunction.exists_right_composable_aux [lemma, in set2]
Bfunction.exists_right_composable_auxC [lemma, in set2]
Bfunction.exists_right_composable_unique [lemma, in set2]
Bfunction.exists_right_composable_uniqueC [lemma, in set2]
Bfunction.exists_right_inv_from_surj [lemma, in set2]
Bfunction.exists_right_inv_from_surjC [lemma, in set2]
Bfunction.exists_unique_left_composable [lemma, in set2]
Bfunction.exists_unique_left_composableC [lemma, in set2]
Bfunction.extends [definition, in set2]
Bfunction.extendsC [definition, in set2]
Bfunction.extendsC_pr [lemma, in set2]
Bfunction.ext_to_prod [definition, in set2]
Bfunction.ext_to_prodC [definition, in set2]
Bfunction.ext_to_prod_bijective [lemma, in set2]
Bfunction.ext_to_prod_function [lemma, in set2]
Bfunction.ext_to_prod_injective [lemma, in set2]
Bfunction.ext_to_prod_inverse [lemma, in set2]
Bfunction.ext_to_prod_prop [lemma, in set2]
Bfunction.ext_to_prod_propJ [lemma, in set2]
Bfunction.ext_to_prod_propP [lemma, in set2]
Bfunction.ext_to_prod_propQ [lemma, in set2]
Bfunction.ext_to_prod_range [lemma, in set2]
Bfunction.ext_to_prod_surjective [lemma, in set2]
Bfunction.ext_to_prod_W [lemma, in set2]
Bfunction.ext_to_prod_W2 [lemma, in set2]
Bfunction.first_proj [definition, in set2]
Bfunction.first_proj_function [lemma, in set2]
Bfunction.first_proj_injective [lemma, in set2]
Bfunction.first_proj_surjective [lemma, in set2]
Bfunction.first_proj_W [lemma, in set2]
Bfunction.functional_graph [definition, in set2]
Bfunction.functionT [inductive, in set2]
Bfunction.functionT_fun [definition, in set2]
Bfunction.function_exten [lemma, in set2]
Bfunction.function_extends_restC [lemma, in set2]
Bfunction.function_extends_restr [lemma, in set2]
Bfunction.function_exten1 [lemma, in set2]
Bfunction.function_exten2 [lemma, in set2]
Bfunction.function_exten3 [lemma, in set2]
Bfunction.function_exten4 [lemma, in set2]
Bfunction.function_fgraph [lemma, in set2]
Bfunction.function_graph [lemma, in set2]
Bfunction.function_rest_of_prolongation [lemma, in set2]
Bfunction.f_domain_graph [lemma, in set2]
Bfunction.f_range_graph [lemma, in set2]
Bfunction.graph_T [lemma, in set2]
Bfunction.identityC [definition, in set2]
Bfunction.identityC_bijective [lemma, in set2]
Bfunction.identity_bijective [lemma, in set2]
Bfunction.identity_function [lemma, in set2]
Bfunction.identity_prop [lemma, in set2]
Bfunction.identity_prop2 [lemma, in set2]
Bfunction.identity_W [lemma, in set2]
Bfunction.imageC [definition, in set2]
Bfunction.imageC_exists [lemma, in set2]
Bfunction.imageC_inc [lemma, in set2]
Bfunction.image_by_fun_source [lemma, in set2]
Bfunction.image_of_fun_pr [lemma, in set2]
Bfunction.image_singleton [lemma, in set2]
Bfunction.inclusionC [definition, in set2]
Bfunction.inclusionC_compose [lemma, in set2]
Bfunction.inclusionC_identity [lemma, in set2]
Bfunction.inclusionC_injective [lemma, in set2]
Bfunction.inclusionC_pr [lemma, in set2]
Bfunction.inc_graph_restriction2 [lemma, in set2]
Bfunction.inc_pr1graph_source [lemma, in set2]
Bfunction.inc_pr1graph_source1 [lemma, in set2]
Bfunction.inc_pr2graph_target [lemma, in set2]
Bfunction.inc_pr2graph_target1 [lemma, in set2]
Bfunction.inc_W_range_graph [lemma, in set2]
Bfunction.inc_W_target [lemma, in set2]
Bfunction.inc_W_targetT [lemma, in set2]
Bfunction.injective [definition, in set2]
Bfunction.injectiveC [definition, in set2]
Bfunction.injective_diag_app [lemma, in set2]
Bfunction.injective_ext_to_prod2C [lemma, in set2]
Bfunction.injective_pr [lemma, in set2]
Bfunction.injective_pr3 [lemma, in set2]
Bfunction.injective_pr_bis [lemma, in set2]
Bfunction.inj_if_exists_left_inv [lemma, in set2]
Bfunction.inj_if_exists_left_invC [lemma, in set2]
Bfunction.inj_is_function [lemma, in set2]
Bfunction.inj_left_compose2 [lemma, in set2]
Bfunction.inj_left_compose2C [lemma, in set2]
Bfunction.inj_right_compose [lemma, in set2]
Bfunction.inj_right_composeC [lemma, in set2]
Bfunction.inverseC [definition, in set2]
Bfunction.inverseC_pra [lemma, in set2]
Bfunction.inverseC_prb [lemma, in set2]
Bfunction.inverseC_prc [lemma, in set2]
Bfunction.inverse_bij_is_bij [lemma, in set2]
Bfunction.inverse_bij_is_bij1 [lemma, in set2]
Bfunction.inverse_direct_image [lemma, in set2]
Bfunction.inverse_direct_image_inj [lemma, in set2]
Bfunction.inverse_ext_to_prod2C [lemma, in set2]
Bfunction.inverse_fun_involutiveC [lemma, in set2]
Bfunction.inv_function_bijective [lemma, in set2]
Bfunction.inv_graph_canon [definition, in set2]
Bfunction.inv_graph_canon_bijective [lemma, in set2]
Bfunction.inv_graph_canon_function [lemma, in set2]
Bfunction.inv_graph_canon_W [lemma, in set2]
Bfunction.inv_image_complement [lemma, in set2]
Bfunction.in_graph_W [lemma, in set2]
Bfunction.is_constant_function [definition, in set2]
Bfunction.is_constant_functionC [definition, in set2]
Bfunction.is_function [definition, in set2]
Bfunction.is_functional [lemma, in set2]
Bfunction.is_function_functional [lemma, in set2]
Bfunction.is_function_pr [lemma, in set2]
Bfunction.is_left_inverse [definition, in set2]
Bfunction.is_left_inverseC [definition, in set2]
Bfunction.is_right_inverse [definition, in set2]
Bfunction.is_right_inverseC [definition, in set2]
Bfunction.left_composable_value [lemma, in set2]
Bfunction.left_composable_valueC [lemma, in set2]
Bfunction.left_inverseC [definition, in set2]
Bfunction.left_inverseC_pr [lemma, in set2]
Bfunction.left_inverse_composable [lemma, in set2]
Bfunction.left_inverse_compose [lemma, in set2]
Bfunction.left_inverse_composeC [lemma, in set2]
Bfunction.left_inverse_comp_id [lemma, in set2]
Bfunction.left_inverse_from_right [lemma, in set2]
Bfunction.left_inverse_from_rightC [lemma, in set2]
Bfunction.left_inverse_surjective [lemma, in set2]
Bfunction.left_inverse_surjectiveC [lemma, in set2]
Bfunction.left_inv_compose_rf [lemma, in set2]
Bfunction.left_inv_compose_rfC [lemma, in set2]
Bfunction.left_inv_compose_rf2 [lemma, in set2]
Bfunction.left_inv_compose_rf2C [lemma, in set2]
Bfunction.pairC [definition, in set2]
Bfunction.partial_fun1 [definition, in set2]
Bfunction.partial_fun1_axioms [lemma, in set2]
Bfunction.partial_fun1_function [lemma, in set2]
Bfunction.partial_fun1_W [lemma, in set2]
Bfunction.partial_fun2 [definition, in set2]
Bfunction.partial_fun2_axioms [lemma, in set2]
Bfunction.partial_fun2_function [lemma, in set2]
Bfunction.partial_fun2_W [lemma, in set2]
Bfunction.prC_prop [lemma, in set2]
Bfunction.prJ_prop [lemma, in set2]
Bfunction.prJ_recov [lemma, in set2]
Bfunction.prop_acreate [lemma, in set2]
Bfunction.prop_bcreate1 [lemma, in set2]
Bfunction.prop_bcreate2 [lemma, in set2]
Bfunction.pr1C [definition, in set2]
Bfunction.pr1C_prop [lemma, in set2]
Bfunction.pr2C [definition, in set2]
Bfunction.pr2C_prop [lemma, in set2]
Bfunction.range_inc_rw [lemma, in set2]
Bfunction.related_inc_source [lemma, in set2]
Bfunction.restriction [definition, in set2]
Bfunction.restrictionC [definition, in set2]
Bfunction.restriction1 [definition, in set2]
Bfunction.restriction1_bijective [lemma, in set2]
Bfunction.restriction1_function [lemma, in set2]
Bfunction.restriction1_pr [lemma, in set2]
Bfunction.restriction1_surjective [lemma, in set2]
Bfunction.restriction1_W [lemma, in set2]
Bfunction.restriction2 [definition, in set2]
Bfunction.restriction2C [definition, in set2]
Bfunction.restriction2C_pr [lemma, in set2]
Bfunction.restriction2C_pr1 [lemma, in set2]
Bfunction.restriction2_axioms [definition, in set2]
Bfunction.restriction2_function [lemma, in set2]
Bfunction.restriction2_graph [lemma, in set2]
Bfunction.restriction2_injective [lemma, in set2]
Bfunction.restriction2_props [lemma, in set2]
Bfunction.restriction2_surjective [lemma, in set2]
Bfunction.restriction2_W [lemma, in set2]
Bfunction.restriction_function [lemma, in set2]
Bfunction.restriction_graph1 [lemma, in set2]
Bfunction.restriction_recovers [lemma, in set2]
Bfunction.restriction_to_image [definition, in set2]
Bfunction.restriction_to_image_pr [lemma, in set2]
Bfunction.restriction_W [lemma, in set2]
Bfunction.restr_domain2 [lemma, in set2]
Bfunction.restr_range [lemma, in set2]
Bfunction.right_composable_value [lemma, in set2]
Bfunction.right_composable_valueC [lemma, in set2]
Bfunction.right_inverseC [definition, in set2]
Bfunction.right_inverse_composable [lemma, in set2]
Bfunction.right_inverse_compose [lemma, in set2]
Bfunction.right_inverse_composeC [lemma, in set2]
Bfunction.right_inverse_comp_id [lemma, in set2]
Bfunction.right_inverse_from_left [lemma, in set2]
Bfunction.right_inverse_from_leftC [lemma, in set2]
Bfunction.right_inverse_injective [lemma, in set2]
Bfunction.right_inverse_injectiveC [lemma, in set2]
Bfunction.right_inverse_pr [lemma, in set2]
Bfunction.right_inv_compose_rf [lemma, in set2]
Bfunction.right_inv_compose_rfC [lemma, in set2]
Bfunction.right_inv_compose_rf2 [lemma, in set2]
Bfunction.right_inv_compose_rf2C [lemma, in set2]
Bfunction.same_graph_agrees [lemma, in set2]
Bfunction.second_proj [definition, in set2]
Bfunction.second_proj_function [lemma, in set2]
Bfunction.second_proj_surjective [lemma, in set2]
Bfunction.second_proj_W [lemma, in set2]
Bfunction.section_unique [lemma, in set2]
Bfunction.section_uniqueC [lemma, in set2]
Bfunction.small_set [definition, in set2]
Bfunction.source_extends [lemma, in set2]
Bfunction.source_right_inverse [lemma, in set2]
Bfunction.source_T [lemma, in set2]
Bfunction.special_empty_function [lemma, in set2]
Bfunction.sub_function [lemma, in set2]
Bfunction.sub_image_target [lemma, in set2]
Bfunction.sub_image_targetC [lemma, in set2]
Bfunction.sub_image_target1 [lemma, in set2]
Bfunction.sub_inv_im_source [lemma, in set2]
Bfunction.surjective [definition, in set2]
Bfunction.surjectiveC [definition, in set2]
Bfunction.surjective_ext_to_prod2C [lemma, in set2]
Bfunction.surjective_pr [lemma, in set2]
Bfunction.surjective_pr2 [lemma, in set2]
Bfunction.surjective_pr3 [lemma, in set2]
Bfunction.surjective_pr4 [lemma, in set2]
Bfunction.surjective_pr5 [lemma, in set2]
Bfunction.surjective_pr6 [lemma, in set2]
Bfunction.surj_if_exists_right_inv [lemma, in set2]
Bfunction.surj_if_exists_right_invC [lemma, in set2]
Bfunction.surj_is_function [lemma, in set2]
Bfunction.surj_left_compose [lemma, in set2]
Bfunction.surj_left_composeC [lemma, in set2]
Bfunction.surj_left_compose2 [lemma, in set2]
Bfunction.surj_left_compose2C [lemma, in set2]
Bfunction.tack_on_corresp [lemma, in set2]
Bfunction.tack_on_f [definition, in set2]
Bfunction.tack_on_function [lemma, in set2]
Bfunction.tack_on_f_injective [lemma, in set2]
Bfunction.tack_on_surjective [lemma, in set2]
Bfunction.tack_on_W_in [lemma, in set2]
Bfunction.tack_on_W_out [lemma, in set2]
Bfunction.target_left_inverse [lemma, in set2]
Bfunction.target_T [lemma, in set2]
Bfunction.transf_axioms [definition, in set2]
Bfunction.W [definition, in set2]
Bfunction.WT [definition, in set2]
Bfunction.w_constant_functionC [lemma, in set2]
Bfunction.W_extends [lemma, in set2]
Bfunction.W_image [lemma, in set2]
Bfunction.W_inverse [lemma, in set2]
Bfunction.W_inverse2 [lemma, in set2]
Bfunction.W_inverse3 [lemma, in set2]
Bfunction.W_left_inverse [lemma, in set2]
Bfunction.w_left_inverse [lemma, in set2]
Bfunction.W_mapping [lemma, in set2]
Bfunction.W_pr [lemma, in set2]
Bfunction.W_pr2 [lemma, in set2]
Bfunction.W_pr3 [lemma, in set2]
Bfunction.w_right_inverse [lemma, in set2]
Bfunction.W_right_inverse [lemma, in set2]
Border [module, in set5]
Border.adjoin_greatest [lemma, in set5]
Border.antisymmetric_r [definition, in set5]
Border.axioms_of_order [lemma, in set5]
Border.bounded_above [definition, in set5]
Border.bounded_above_sub [lemma, in set5]
Border.bounded_below [definition, in set5]
Border.bounded_below_sub [lemma, in set5]
Border.bounded_both [definition, in set5]
Border.bounded_both_sub [lemma, in set5]
Border.coarser [definition, in set5]
Border.coarser_order [lemma, in set5]
Border.coarser_preorder [definition, in set5]
Border.coarser_preorder_order [lemma, in set5]
Border.coarser_preorder_related [lemma, in set5]
Border.coarser_preorder_related1 [lemma, in set5]
Border.coarser_preorder_substrate [lemma, in set5]
Border.coarser_related [lemma, in set5]
Border.coarser_related_bis [lemma, in set5]
Border.coarser_substrate [lemma, in set5]
Border.cofinal_right_directed [lemma, in set5]
Border.cofinal_set [definition, in set5]
Border.coinitial_left_directed [lemma, in set5]
Border.coinitial_set [definition, in set5]
Border.compare_inf_sup1 [lemma, in set5]
Border.compare_inf_sup2 [lemma, in set5]
Border.compatible_equivalence_preorder [lemma, in set5]
Border.compatible_equivalence_preorder1 [lemma, in set5]
Border.compatible_equivalence_pre_order [lemma, in set5]
Border.complementary_decreasing [lemma, in set5]
Border.compose3_related [lemma, in set5]
Border.constant_fun_decreasing [lemma, in set5]
Border.constant_fun_increasing [lemma, in set5]
Border.cst_graph [definition, in set5]
Border.cst_graph_pr [lemma, in set5]
Border.decreasing_composition [lemma, in set5]
Border.decreasing_fun [definition, in set5]
Border.decreasing_fun_from_strict [lemma, in set5]
Border.decreasing_fun_reva [lemma, in set5]
Border.decreasing_fun_revb [lemma, in set5]
Border.diagonal_order [lemma, in set5]
Border.emptyset_is_least [lemma, in set5]
Border.empty_function_tg [definition, in set5]
Border.empty_function_tg_function [lemma, in set5]
Border.empty_interval [lemma, in set5]
Border.equality_is_order [lemma, in set5]
Border.equivalence_associated_o [definition, in set5]
Border.equivalence_preorder [lemma, in set5]
Border.equivalence_preorder1 [lemma, in set5]
Border.exists_greatest_cofinal [lemma, in set5]
Border.exists_least_coinitial [lemma, in set5]
Border.extends_in_prop [lemma, in set5]
Border.extension_is_order [lemma, in set5]
Border.extension_order [definition, in set5]
Border.extension_order_pr [lemma, in set5]
Border.extension_order_pr1 [lemma, in set5]
Border.extension_order_pr2 [lemma, in set5]
Border.extension_order_rw [lemma, in set5]
Border.fam_of_substrates [definition, in set5]
Border.function_order [definition, in set5]
Border.function_order_isomorphism [lemma, in set5]
Border.function_order_order [lemma, in set5]
Border.function_order_pr [lemma, in set5]
Border.function_order_r [definition, in set5]
Border.function_order_reflexive [lemma, in set5]
Border.function_order_substrate [lemma, in set5]
Border.gge [definition, in set5]
Border.ggt [definition, in set5]
Border.ggt_inva [lemma, in set5]
Border.ggt_invb [lemma, in set5]
Border.gle [definition, in set5]
Border.glt [definition, in set5]
Border.glt_inva [lemma, in set5]
Border.gop_axioms [lemma, in set5]
Border.gop_morphism [lemma, in set5]
Border.gop_W [lemma, in set5]
Border.graph_of_function [definition, in set5]
Border.graph_of_function_axioms [lemma, in set5]
Border.graph_of_function_bijective [lemma, in set5]
Border.graph_of_function_fonction [lemma, in set5]
Border.graph_of_function_isomorphism [lemma, in set5]
Border.graph_of_function_sub [lemma, in set5]
Border.graph_of_function_W [lemma, in set5]
Border.graph_of_partition [definition, in set5]
Border.graph_on_rw3 [lemma, in set5]
Border.graph_order [definition, in set5]
Border.graph_order_order [lemma, in set5]
Border.graph_order_pr [lemma, in set5]
Border.graph_order_pr1 [lemma, in set5]
Border.graph_order_r [definition, in set5]
Border.graph_order_r_pr [lemma, in set5]
Border.graph_order_substrate [lemma, in set5]
Border.greater_upper_bound [lemma, in set5]
Border.greatest_element [definition, in set5]
Border.greatest_element_pr [lemma, in set5]
Border.greatest_induced [lemma, in set5]
Border.greatest_is_sup [lemma, in set5]
Border.greatest_is_union [lemma, in set5]
Border.greatest_lower_bound [definition, in set5]
Border.greatest_lower_bound_doubleton [lemma, in set5]
Border.greatest_lower_bound_emptyset [lemma, in set5]
Border.greatest_lower_bound_pr [lemma, in set5]
Border.greatest_maximal [lemma, in set5]
Border.greatest_prolongation [lemma, in set5]
Border.greatest_reverse [lemma, in set5]
Border.greatest_right_directed [lemma, in set5]
Border.greatest_unique_maximal [lemma, in set5]
Border.has_infimum [definition, in set5]
Border.has_inf_graph [definition, in set5]
Border.has_supremum [definition, in set5]
Border.has_sup_graph [definition, in set5]
Border.identity_increasing_decreasing [lemma, in set5]
Border.inclusion_is_order [lemma, in set5]
Border.inclusion_order [definition, in set5]
Border.inclusion_order_rw [lemma, in set5]
Border.inclusion_suborder [definition, in set5]
Border.increasing_fun [definition, in set5]
Border.increasing_fun_from_strict [lemma, in set5]
Border.increasing_fun_reva [lemma, in set5]
Border.increasing_fun_revb [lemma, in set5]
Border.inc_infimum_substrate [lemma, in set5]
Border.inc_supremum_substrate [lemma, in set5]
Border.induced_order [definition, in set5]
Border.induced_order_substrate [lemma, in set5]
Border.inf [definition, in set5]
Border.infimum [definition, in set5]
Border.infimum_pr [lemma, in set5]
Border.infimum_pr1 [lemma, in set5]
Border.infimum_pr2 [lemma, in set5]
Border.infimum_unique [lemma, in set5]
Border.inf_comparable [lemma, in set5]
Border.inf_comparable1 [lemma, in set5]
Border.inf_decreasing [lemma, in set5]
Border.inf_decreasing1 [lemma, in set5]
Border.inf_distributive [lemma, in set5]
Border.inf_distributive1 [lemma, in set5]
Border.inf_distributive2 [lemma, in set5]
Border.inf_distributive3 [lemma, in set5]
Border.inf_graph [definition, in set5]
Border.inf_inclusion [lemma, in set5]
Border.inf_increasing2 [lemma, in set5]
Border.inf_induced1 [lemma, in set5]
Border.inf_induced2 [lemma, in set5]
Border.inf_in_product [lemma, in set5]
Border.inf_in_total_order [lemma, in set5]
Border.inf_pr [lemma, in set5]
Border.inf_sup_opp [lemma, in set5]
Border.intersection4 [lemma, in set5]
Border.intersection_interval [lemma, in set5]
Border.intersection_is_inf [lemma, in set5]
Border.intersection_is_inf1 [lemma, in set5]
Border.intersection_is_least [lemma, in set5]
Border.intersection_i1 [lemma, in set5]
Border.intersection_i2 [lemma, in set5]
Border.intersection_i3 [lemma, in set5]
Border.interval_cc [definition, in set5]
Border.interval_co [definition, in set5]
Border.interval_cu [definition, in set5]
Border.interval_oc [definition, in set5]
Border.interval_oo [definition, in set5]
Border.interval_ou [definition, in set5]
Border.interval_uc [definition, in set5]
Border.interval_uo [definition, in set5]
Border.interval_uu [definition, in set5]
Border.inter_rel_order [lemma, in set5]
Border.is_antisymmetric [definition, in set5]
Border.is_bounded_interval [definition, in set5]
Border.is_closed_interval [definition, in set5]
Border.is_inf_fun [definition, in set5]
Border.is_inf_fun_pr [lemma, in set5]
Border.is_inf_graph [definition, in set5]
Border.is_inf_graph_pr [lemma, in set5]
Border.is_inf_graph_pr1 [lemma, in set5]
Border.is_interval [definition, in set5]
Border.is_left_unbounded_interval [definition, in set5]
Border.is_lu_interval [definition, in set5]
Border.is_open_interval [definition, in set5]
Border.is_right_unbounded_interval [definition, in set5]
Border.is_ru_interval [definition, in set5]
Border.is_semi_open_interval [definition, in set5]
Border.is_sup_fun [definition, in set5]
Border.is_sup_fun_pr [lemma, in set5]
Border.is_sup_graph [definition, in set5]
Border.is_sup_graph_pr [lemma, in set5]
Border.is_sup_graph_pr1 [lemma, in set5]
Border.is_unbounded_interval [definition, in set5]
Border.largest_partition_is_largest [lemma, in set5]
Border.lattice [definition, in set5]
Border.lattice_directed [lemma, in set5]
Border.lattice_inf_pr [lemma, in set5]
Border.lattice_inverse [lemma, in set5]
Border.lattice_sup_pr [lemma, in set5]
Border.least_element [definition, in set5]
Border.least_element_pr [lemma, in set5]
Border.least_equivalence [lemma, in set5]
Border.least_induced [lemma, in set5]
Border.least_is_inf [lemma, in set5]
Border.least_is_intersection [lemma, in set5]
Border.least_left_directed [lemma, in set5]
Border.least_minimal [lemma, in set5]
Border.least_not_greatest [lemma, in set5]
Border.least_prolongation [lemma, in set5]
Border.least_reverse [lemma, in set5]
Border.least_unique_minimal [lemma, in set5]
Border.least_upper_bound [definition, in set5]
Border.least_upper_bound_doubleton [lemma, in set5]
Border.least_upper_bound_emptyset [lemma, in set5]
Border.least_upper_bound_pr [lemma, in set5]
Border.left_directed [definition, in set5]
Border.left_directed_mimimal [lemma, in set5]
Border.left_directed_pr [lemma, in set5]
Border.leq_lt_trans [lemma, in set5]
Border.le_pr [lemma, in set5]
Border.lower_bound [definition, in set5]
Border.lt_leq_trans [lemma, in set5]
Border.lt_lt_trans [lemma, in set5]
Border.maximal_element [definition, in set5]
Border.maximal_element_opp [lemma, in set5]
Border.maximal_opposite [lemma, in set5]
Border.maximal_prolongation [lemma, in set5]
Border.minimal_element [definition, in set5]
Border.minimal_element_opp [lemma, in set5]
Border.minimal_inclusion [lemma, in set5]
Border.monotone_fun [definition, in set5]
Border.monotone_fun_reva [lemma, in set5]
Border.monotone_fun_revb [lemma, in set5]
Border.nondisjoint [lemma, in set5]
Border.nonempty_closed_interval [lemma, in set5]
Border.not_le_gt [lemma, in set5]
Border.opposite_gge [lemma, in set5]
Border.opposite_gle [lemma, in set5]
Border.opposite_induced [lemma, in set5]
Border.opposite_is_order [lemma, in set5]
Border.opposite_is_order_r [lemma, in set5]
Border.opposite_is_preorder1 [lemma, in set5]
Border.opposite_is_preorder_r [lemma, in set5]
Border.opposite_left_directed [lemma, in set5]
Border.opposite_lower_bound [lemma, in set5]
Border.opposite_order [definition, in set5]
Border.opposite_relation [definition, in set5]
Border.opposite_right_directed [lemma, in set5]
Border.opposite_upper_bound [lemma, in set5]
Border.order [definition, in set5]
Border.order_antisymmetry [lemma, in set5]
Border.order_associated [definition, in set5]
Border.order_associated_graph [lemma, in set5]
Border.order_associated_order [lemma, in set5]
Border.order_associated_pr [lemma, in set5]
Border.order_associated_related1 [lemma, in set5]
Border.order_associated_related2 [lemma, in set5]
Border.order_associated_substrate [lemma, in set5]
Border.order_axioms [definition, in set5]
Border.order_from_rel [lemma, in set5]
Border.order_from_rel1 [lemma, in set5]
Border.order_has_graph [lemma, in set5]
Border.order_has_graph0 [lemma, in set5]
Border.order_has_graph2 [lemma, in set5]
Border.order_if_has_graph [lemma, in set5]
Border.order_if_has_graph2 [lemma, in set5]
Border.order_induced_order [lemma, in set5]
Border.order_isomorphism [definition, in set5]
Border.order_isomorphism_increasing [lemma, in set5]
Border.order_isomorphism_opposite [lemma, in set5]
Border.order_isomorphism_pr [lemma, in set5]
Border.order_is_graph [lemma, in set5]
Border.order_is_order [lemma, in set5]
Border.order_morphism [definition, in set5]
Border.order_morphism_increasing [lemma, in set5]
Border.order_pr [lemma, in set5]
Border.order_preorder [lemma, in set5]
Border.order_r [definition, in set5]
Border.order_re [definition, in set5]
Border.order_reflexivity [lemma, in set5]
Border.order_reflexivity_pr [lemma, in set5]
Border.order_symmetricity_pr [lemma, in set5]
Border.order_transitivity [lemma, in set5]
Border.order_transportation [lemma, in set5]
Border.order_with_greatest [definition, in set5]
Border.order_with_greatest_pr [lemma, in set5]
Border.partial_fun [definition, in set5]
Border.partition_fun_of_set [definition, in set5]
Border.partition_relation_set [definition, in set5]
Border.partition_relation_set_aux [definition, in set5]
Border.partition_relation_set_order [lemma, in set5]
Border.partition_relation_set_order_antisymmetric [lemma, in set5]
Border.partition_relation_set_pr [lemma, in set5]
Border.partition_relation_set_pr1 [lemma, in set5]
Border.partition_set_in_double_powerset [lemma, in set5]
Border.pfs_function [lemma, in set5]
Border.pfs_partition [lemma, in set5]
Border.pfs_W [lemma, in set5]
Border.powerset_lattice [lemma, in set5]
Border.preorder [definition, in set5]
Border.preorder_from_rel [lemma, in set5]
Border.preorder_graph [lemma, in set5]
Border.preorder_induced_order [lemma, in set5]
Border.preorder_is_preorder [lemma, in set5]
Border.preorder_prop [lemma, in set5]
Border.preorder_prop1 [lemma, in set5]
Border.preorder_prop2 [lemma, in set5]
Border.preorder_r [definition, in set5]
Border.preorder_reflexivity [lemma, in set5]
Border.product2_order [definition, in set5]
Border.product2_order_order [lemma, in set5]
Border.product2_order_pr [lemma, in set5]
Border.product2_order_preorder [lemma, in set5]
Border.product2_order_preorder_substrate [lemma, in set5]
Border.product2_order_substrate [lemma, in set5]
Border.product_lattice [lemma, in set5]
Border.product_left_directed [lemma, in set5]
Border.product_order [definition, in set5]
Border.product_order_axioms [definition, in set5]
Border.product_order_axioms_x [lemma, in set5]
Border.product_order_def [lemma, in set5]
Border.product_order_order [lemma, in set5]
Border.product_order_r [definition, in set5]
Border.product_order_related [lemma, in set5]
Border.product_order_substrate [lemma, in set5]
Border.product_right_directed [lemma, in set5]
Border.prod_of_substrates [definition, in set5]
Border.prod_of_substrates_rw [lemma, in set5]
Border.prs_is_equivalence [lemma, in set5]
Border.reflexive_induced_order [lemma, in set5]
Border.reflexive_rr [definition, in set5]
Border.related_induced_order [lemma, in set5]
Border.related_induced_order1 [lemma, in set5]
Border.related_induced_order2 [lemma, in set5]
Border.related_induced_order3 [lemma, in set5]
Border.related_induced_order4 [lemma, in set5]
Border.relation_induced_order [lemma, in set5]
Border.right_directed [definition, in set5]
Border.right_directed_maximal [lemma, in set5]
Border.right_directed_pr [lemma, in set5]
Border.set_of_fgraphs [definition, in set5]
Border.set_of_graphs_pr [lemma, in set5]
Border.set_of_lower_bounds_emptyset [lemma, in set5]
Border.set_of_majorants1 [definition, in set5]
Border.set_of_majorants1_decreasing [lemma, in set5]
Border.set_of_majorants1_pr [lemma, in set5]
Border.set_of_partition_rw [lemma, in set5]
Border.set_of_partition_set [definition, in set5]
Border.set_of_preorders [definition, in set5]
Border.set_of_preorders_rw [lemma, in set5]
Border.set_of_upper_bounds_emptyset [lemma, in set5]
Border.singleton_bounded [lemma, in set5]
Border.singleton_interval [lemma, in set5]
Border.singleton_pr [lemma, in set5]
Border.smaller_lower_bound [lemma, in set5]
Border.smallest_partition_is_smallest [lemma, in set5]
Border.strict_decreasing_from_injective [lemma, in set5]
Border.strict_decreasing_fun [definition, in set5]
Border.strict_decreasing_fun_reva [lemma, in set5]
Border.strict_decreasing_fun_revb [lemma, in set5]
Border.strict_increasing_from_injective [lemma, in set5]
Border.strict_increasing_fun [definition, in set5]
Border.strict_increasing_fun_reva [lemma, in set5]
Border.strict_increasing_fun_revb [lemma, in set5]
Border.strict_monotone_from_injective [lemma, in set5]
Border.strict_monotone_fun [definition, in set5]
Border.strict_monotone_fun_reva [lemma, in set5]
Border.strict_monotone_fun_revb [lemma, in set5]
Border.subinclusion_is_order [lemma, in set5]
Border.subinclusion_order_rw [lemma, in set5]
Border.substrate_domain_order [lemma, in set5]
Border.substrate_equivalence_associated_o [lemma, in set5]
Border.substrate_extension_order [lemma, in set5]
Border.substrate_graph_on [lemma, in set5]
Border.substrate_inclusion_order [lemma, in set5]
Border.substrate_induced_order [lemma, in set5]
Border.substrate_induced_order1 [lemma, in set5]
Border.substrate_opposite_order [lemma, in set5]
Border.substrate_subinclusion_order [lemma, in set5]
Border.sub_is_order [lemma, in set5]
Border.sub_lower_bound [lemma, in set5]
Border.sub_partition_relation_set_coarse [lemma, in set5]
Border.sub_upper_bound [lemma, in set5]
Border.sup [definition, in set5]
Border.supremum [definition, in set5]
Border.supremum_pr [lemma, in set5]
Border.supremum_pr1 [lemma, in set5]
Border.supremum_pr2 [lemma, in set5]
Border.supremum_unique [lemma, in set5]
Border.sup_comparable [lemma, in set5]
Border.sup_comparable1 [lemma, in set5]
Border.sup_distributive [lemma, in set5]
Border.sup_distributive1 [lemma, in set5]
Border.sup_distributive2 [lemma, in set5]
Border.sup_distributive3 [lemma, in set5]
Border.sup_extension_order1 [lemma, in set5]
Border.sup_extension_order2 [lemma, in set5]
Border.sup_graph [definition, in set5]
Border.sup_inclusion [lemma, in set5]
Border.sup_increasing [lemma, in set5]
Border.sup_increasing1 [lemma, in set5]
Border.sup_increasing2 [lemma, in set5]
Border.sup_induced1 [lemma, in set5]
Border.sup_induced2 [lemma, in set5]
Border.sup_inf_opp [lemma, in set5]
Border.sup_in_product [lemma, in set5]
Border.sup_in_total_order [lemma, in set5]
Border.sup_pr [lemma, in set5]
Border.the_greatest_element [definition, in set5]
Border.the_greatest_element_pr [lemma, in set5]
Border.the_greatest_element_pr2 [lemma, in set5]
Border.the_greatest_interval [lemma, in set5]
Border.the_least_element [definition, in set5]
Border.the_least_element_pr [lemma, in set5]
Border.the_least_element_pr2 [lemma, in set5]
Border.the_least_interval [lemma, in set5]
Border.the_least_reverse [lemma, in set5]
Border.total_order [definition, in set5]
Border.total_order_conterexample [lemma, in set5]
Border.total_order_directed [lemma, in set5]
Border.total_order_increasing_morphism [lemma, in set5]
Border.total_order_lattice [lemma, in set5]
Border.total_order_monotone_injective [lemma, in set5]
Border.total_order_opposite [lemma, in set5]
Border.total_order_pr [lemma, in set5]
Border.total_order_pr1 [lemma, in set5]
Border.total_order_pr2 [lemma, in set5]
Border.total_order_small [lemma, in set5]
Border.total_order_sub [lemma, in set5]
Border.transitive_induced_order [lemma, in set5]
Border.union_is_greatest [lemma, in set5]
Border.union_is_sup [lemma, in set5]
Border.union_is_sup1 [lemma, in set5]
Border.unique_greatest [lemma, in set5]
Border.unique_least [lemma, in set5]
Border.upper_bound [definition, in set5]
Border.wholeset_is_greatest [lemma, in set5]
Bproduct [module, in set3]
Bproduct.cf_injective [lemma, in set3]
Bproduct.complementary_intersection1 [lemma, in set3]
Bproduct.complementary_union1 [lemma, in set3]
Bproduct.compose_V [lemma, in set3]
Bproduct.constant_functor [definition, in set3]
Bproduct.constant_graph [definition, in set3]
Bproduct.constant_graph_function [lemma, in set3]
Bproduct.constant_graph_is_constant [lemma, in set3]
Bproduct.constant_graph_small_range [lemma, in set3]
Bproduct.constant_graph_V [lemma, in set3]
Bproduct.diagonal_graphp [definition, in set3]
Bproduct.diagonal_graph_rw [lemma, in set3]
Bproduct.distrib_inter2_union [lemma, in set3]
Bproduct.distrib_inter_prod [lemma, in set3]
Bproduct.distrib_inter_prod_inter [lemma, in set3]
Bproduct.distrib_inter_union [lemma, in set3]
Bproduct.distrib_product2_inter [lemma, in set3]
Bproduct.distrib_product2_union [lemma, in set3]
Bproduct.distrib_prod2_inter [lemma, in set3]
Bproduct.distrib_prod2_union [lemma, in set3]
Bproduct.distrib_prod_intersection [lemma, in set3]
Bproduct.distrib_prod_inter2_prod [lemma, in set3]
Bproduct.distrib_prod_union [lemma, in set3]
Bproduct.distrib_union2_inter [lemma, in set3]
Bproduct.distrib_union_inter [lemma, in set3]
Bproduct.extension_partial_product [lemma, in set3]
Bproduct.ext_map_prod [definition, in set3]
Bproduct.ext_map_prod_aux [definition, in set3]
Bproduct.ext_map_prod_axioms [definition, in set3]
Bproduct.ext_map_prod_composable [lemma, in set3]
Bproduct.ext_map_prod_compose [lemma, in set3]
Bproduct.ext_map_prod_function [lemma, in set3]
Bproduct.ext_map_prod_injective [lemma, in set3]
Bproduct.ext_map_prod_surjective [lemma, in set3]
Bproduct.ext_map_prod_taxioms [lemma, in set3]
Bproduct.ext_map_prod_W [lemma, in set3]
Bproduct.ext_map_prod_WV [lemma, in set3]
Bproduct.first_proj_bijective [lemma, in set3]
Bproduct.fun_set_to_prod [definition, in set3]
Bproduct.fun_set_to_prod1 [lemma, in set3]
Bproduct.fun_set_to_prod2 [lemma, in set3]
Bproduct.fun_set_to_prod3 [lemma, in set3]
Bproduct.fun_set_to_prod4 [lemma, in set3]
Bproduct.fun_set_to_prod5 [definition, in set3]
Bproduct.fun_set_to_prod6 [lemma, in set3]
Bproduct.fun_set_to_prod7 [lemma, in set3]
Bproduct.fun_set_to_prod8 [lemma, in set3]
Bproduct.gbcreate [definition, in set3]
Bproduct.gbcreate_domain [lemma, in set3]
Bproduct.gbcreate_fgraph [lemma, in set3]
Bproduct.gbcreate_graph [lemma, in set3]
Bproduct.gbcreate_rw [lemma, in set3]
Bproduct.gbcreate_V [lemma, in set3]
Bproduct.graphset_pr1 [lemma, in set3]
Bproduct.graphset_pr2 [lemma, in set3]
Bproduct.graph_exten [lemma, in set3]
Bproduct.intersectionf_singleton [lemma, in set3]
Bproduct.is_constant_graph [definition, in set3]
Bproduct.is_singleton [definition, in set3]
Bproduct.is_singleton_rw [lemma, in set3]
Bproduct.nonempty_from_domain [lemma, in set3]
Bproduct.nonempty_product3 [lemma, in set3]
Bproduct.pam_axioms [lemma, in set3]
Bproduct.pam_bijective [lemma, in set3]
Bproduct.pam_function [lemma, in set3]
Bproduct.pam_injective [lemma, in set3]
Bproduct.pam_W [lemma, in set3]
Bproduct.partition_product [lemma, in set3]
Bproduct.pc_axioms [lemma, in set3]
Bproduct.pc_axioms0 [lemma, in set3]
Bproduct.pc_bijective [lemma, in set3]
Bproduct.pc_function [lemma, in set3]
Bproduct.pc_W [lemma, in set3]
Bproduct.pc_WV [lemma, in set3]
Bproduct.popc_axioms [lemma, in set3]
Bproduct.popc_bijection [lemma, in set3]
Bproduct.popc_target [lemma, in set3]
Bproduct.popc_target_aux [lemma, in set3]
Bproduct.popc_W [lemma, in set3]
Bproduct.pri_axioms [lemma, in set3]
Bproduct.pri_function [lemma, in set3]
Bproduct.pri_surjective [lemma, in set3]
Bproduct.pri_W [lemma, in set3]
Bproduct.prj_axioms [lemma, in set3]
Bproduct.prj_bijective [lemma, in set3]
Bproduct.prj_function [lemma, in set3]
Bproduct.prj_surjective [lemma, in set3]
Bproduct.prj_W [lemma, in set3]
Bproduct.prj_WV [lemma, in set3]
Bproduct.productb [definition, in set3]
Bproduct.productb_exten [lemma, in set3]
Bproduct.productb_monotone1 [lemma, in set3]
Bproduct.productb_monotone2 [lemma, in set3]
Bproduct.productb_rw [lemma, in set3]
Bproduct.productf [definition, in set3]
Bproduct.productf_exten [lemma, in set3]
Bproduct.productf_extension [lemma, in set3]
Bproduct.productf_rw [lemma, in set3]
Bproduct.productt [definition, in set3]
Bproduct.productt_exten [lemma, in set3]
Bproduct.productt_nonempty [lemma, in set3]
Bproduct.productt_nonempty2 [lemma, in set3]
Bproduct.productt_rw [lemma, in set3]
Bproduct.product1 [definition, in set3]
Bproduct.product1_canon [definition, in set3]
Bproduct.product1_canon_axioms [lemma, in set3]
Bproduct.product1_canon_bijective [lemma, in set3]
Bproduct.product1_canon_function [lemma, in set3]
Bproduct.product1_canon_W [lemma, in set3]
Bproduct.product1_pr [lemma, in set3]
Bproduct.product1_pr2 [lemma, in set3]
Bproduct.product1_rw [lemma, in set3]
Bproduct.product2 [definition, in set3]
Bproduct.product2_canon [definition, in set3]
Bproduct.product2_canon_axioms [lemma, in set3]
Bproduct.product2_canon_bijective [lemma, in set3]
Bproduct.product2_canon_function [lemma, in set3]
Bproduct.product2_canon_W [lemma, in set3]
Bproduct.product2_rw [lemma, in set3]
Bproduct.product2_trivial [lemma, in set3]
Bproduct.product_compose [definition, in set3]
Bproduct.product_eq_graphset [lemma, in set3]
Bproduct.product_nonempty [lemma, in set3]
Bproduct.product_nonempty2 [lemma, in set3]
Bproduct.product_singleton [lemma, in set3]
Bproduct.product_sub_graphset [lemma, in set3]
Bproduct.product_trivial [lemma, in set3]
Bproduct.prod_assoc_axioms [definition, in set3]
Bproduct.prod_assoc_map [definition, in set3]
Bproduct.prod_assoc_map2 [lemma, in set3]
Bproduct.prod_of_function [definition, in set3]
Bproduct.prod_of_function_axioms [lemma, in set3]
Bproduct.prod_of_function_function [lemma, in set3]
Bproduct.prod_of_function_W [lemma, in set3]
Bproduct.prod_of_products [definition, in set3]
Bproduct.prod_of_products_canon [definition, in set3]
Bproduct.prod_of_products_fam_pr [lemma, in set3]
Bproduct.prod_of_products_function [lemma, in set3]
Bproduct.prod_of_products_source [lemma, in set3]
Bproduct.prod_of_products_target [lemma, in set3]
Bproduct.prod_of_products_W [lemma, in set3]
Bproduct.prod_of_product_aux [definition, in set3]
Bproduct.prod_of_prod_inc_target [lemma, in set3]
Bproduct.prod_of_prod_target [definition, in set3]
Bproduct.pr_i [definition, in set3]
Bproduct.pr_it [definition, in set3]
Bproduct.pr_j [definition, in set3]
Bproduct.restriction_graph2 [lemma, in set3]
Bproduct.restriction_product [definition, in set3]
Bproduct.trivial_fgraph [lemma, in set3]
Bproduct.trivial_product1 [lemma, in set3]
Bproduct.unionf_emptyset [lemma, in set3]
Bproduct.unionf_singleton [lemma, in set3]
Bproduct.variantLc_prop [lemma, in set3]
Bproduct.variant_if_not_rw1 [lemma, in set3]
Bproduct.variant_if_rw1 [lemma, in set3]
Bunion [module, in set3]
Bunion.agrees_on_covering [lemma, in set3]
Bunion.coarser_antisymmetric [lemma, in set3]
Bunion.coarser_c [definition, in set3]
Bunion.coarser_covering [definition, in set3]
Bunion.coarser_reflexive [lemma, in set3]
Bunion.coarser_same [lemma, in set3]
Bunion.coarser_transitive [lemma, in set3]
Bunion.complementary_intersection [lemma, in set3]
Bunion.complementary_union [lemma, in set3]
Bunion.composable_for_function [lemma, in set3]
Bunion.compose3function [definition, in set3]
Bunion.constant_function_pr [lemma, in set3]
Bunion.covering [definition, in set3]
Bunion.covering_f [definition, in set3]
Bunion.covering_f_pr [lemma, in set3]
Bunion.covering_pr [lemma, in set3]
Bunion.covering_s [definition, in set3]
Bunion.c3f_axioms [lemma, in set3]
Bunion.c3f_bijective [lemma, in set3]
Bunion.c3f_function [lemma, in set3]
Bunion.c3f_injective [lemma, in set3]
Bunion.c3f_surjective [lemma, in set3]
Bunion.c3f_W [lemma, in set3]
Bunion.disjoint [definition, in set3]
Bunion.disjoint_complement [lemma, in set3]
Bunion.disjoint_pr [lemma, in set3]
Bunion.disjoint_symmetric [lemma, in set3]
Bunion.disjoint_union [definition, in set3]
Bunion.disjoint_union_disjoint [lemma, in set3]
Bunion.disjoint_union_fam [definition, in set3]
Bunion.disjoint_union_lemma [lemma, in set3]
Bunion.disjoint_union_pr [lemma, in set3]
Bunion.empty_set_of_functions_target [lemma, in set3]
Bunion.empty_source_graph [lemma, in set3]
Bunion.empty_target_graph [lemma, in set3]
Bunion.empty_unionf [lemma, in set3]
Bunion.empty_unionf1 [lemma, in set3]
Bunion.empty_uniont1 [lemma, in set3]
Bunion.etp_axioms [lemma, in set3]
Bunion.etp_composable [lemma, in set3]
Bunion.etp_compose [lemma, in set3]
Bunion.etp_function [lemma, in set3]
Bunion.etp_identity [lemma, in set3]
Bunion.etp_injective [lemma, in set3]
Bunion.etp_surjective [lemma, in set3]
Bunion.etp_W [lemma, in set3]
Bunion.extension_covering [lemma, in set3]
Bunion.extension_covering1 [lemma, in set3]
Bunion.extension_partition [lemma, in set3]
Bunion.extension_partition1 [lemma, in set3]
Bunion.extension_to_parts [definition, in set3]
Bunion.first_partial_fun [definition, in set3]
Bunion.first_partial_function [definition, in set3]
Bunion.first_partial_map [definition, in set3]
Bunion.fpfa_axioms [lemma, in set3]
Bunion.fpfa_bijective [lemma, in set3]
Bunion.fpfa_function [lemma, in set3]
Bunion.fpfa_W [lemma, in set3]
Bunion.fpfb_axioms [lemma, in set3]
Bunion.fpfb_function [lemma, in set3]
Bunion.fpfb_W [lemma, in set3]
Bunion.fpfb_WW [lemma, in set3]
Bunion.fpf_axioms [lemma, in set3]
Bunion.fpf_function [lemma, in set3]
Bunion.fpf_W [lemma, in set3]
Bunion.function_prop [definition, in set3]
Bunion.function_prop_sub [definition, in set3]
Bunion.graph_axioms [lemma, in set3]
Bunion.graph_bijective [lemma, in set3]
Bunion.image_of_covering [lemma, in set3]
Bunion.image_of_intersection [lemma, in set3]
Bunion.image_of_intersection2 [lemma, in set3]
Bunion.image_of_union [lemma, in set3]
Bunion.image_of_union2 [lemma, in set3]
Bunion.inc_set_of_gfunctions [lemma, in set3]
Bunion.injective_graph [definition, in set3]
Bunion.injective_partition [lemma, in set3]
Bunion.inj_image_of_comp [lemma, in set3]
Bunion.inj_image_of_intersection [lemma, in set3]
Bunion.inj_image_of_intersection2 [lemma, in set3]
Bunion.intersectionb [definition, in set3]
Bunion.intersectionb_empty [lemma, in set3]
Bunion.intersectionb_extensionality [lemma, in set3]
Bunion.intersectionb_forall [lemma, in set3]
Bunion.intersectionb_inc [lemma, in set3]
Bunion.intersectionb_rewrite [lemma, in set3]
Bunion.intersectionb_rw [lemma, in set3]
Bunion.intersectionf [definition, in set3]
Bunion.intersectionf_empty [lemma, in set3]
Bunion.intersectionf_extensionality [lemma, in set3]
Bunion.intersectionf_forall [lemma, in set3]
Bunion.intersectionf_inc [lemma, in set3]
Bunion.intersectionf_rw [lemma, in set3]
Bunion.intersectionf_singleton [lemma, in set3]
Bunion.intersectiont [definition, in set3]
Bunion.intersectiont_constant [lemma, in set3]
Bunion.intersectiont_constant_alt [lemma, in set3]
Bunion.intersectiont_empty [lemma, in set3]
Bunion.intersectiont_extensionality [lemma, in set3]
Bunion.intersectiont_forall [lemma, in set3]
Bunion.intersectiont_inc [lemma, in set3]
Bunion.intersectiont_rewrite [lemma, in set3]
Bunion.intersectiont_rw [lemma, in set3]
Bunion.intersectiont_singleton [lemma, in set3]
Bunion.intersectiont_sub [lemma, in set3]
Bunion.intersectiont_sub2 [lemma, in set3]
Bunion.intersection2assoc [lemma, in set3]
Bunion.intersection2_comp [lemma, in set3]
Bunion.intersection2_complement [lemma, in set3]
Bunion.intersection_assoc [lemma, in set3]
Bunion.intersection_covering [definition, in set3]
Bunion.intersection_covering2 [definition, in set3]
Bunion.intersection_covering2_pr [lemma, in set3]
Bunion.intersection_covering_coarser1 [lemma, in set3]
Bunion.intersection_covering_coarser2 [lemma, in set3]
Bunion.intersection_covering_coarser3 [lemma, in set3]
Bunion.intersection_cov_coarser1 [lemma, in set3]
Bunion.intersection_cov_coarser2 [lemma, in set3]
Bunion.intersection_cov_coarser3 [lemma, in set3]
Bunion.intersection_is_covering [lemma, in set3]
Bunion.intersection_monotone [lemma, in set3]
Bunion.intersection_monotone2 [lemma, in set3]
Bunion.intersection_of_twosets [lemma, in set3]
Bunion.intersection_of_twosets_aux [lemma, in set3]
Bunion.intersection_prop [lemma, in set3]
Bunion.intersection_singleton [lemma, in set3]
Bunion.intersection_union_distrib1 [lemma, in set3]
Bunion.intersection_union_distrib2 [lemma, in set3]
Bunion.inv_image_disjoint [lemma, in set3]
Bunion.inv_image_of_comp [lemma, in set3]
Bunion.inv_image_of_covering [lemma, in set3]
Bunion.inv_image_of_intersection [lemma, in set3]
Bunion.inv_image_of_intersection2 [lemma, in set3]
Bunion.is_partition_with_complement [lemma, in set3]
Bunion.largest_partition [definition, in set3]
Bunion.largest_partition_pr [lemma, in set3]
Bunion.mutually_disjoint [definition, in set3]
Bunion.mutually_disjoint_prop [lemma, in set3]
Bunion.mutually_disjoint_prop2 [lemma, in set3]
Bunion.nonemptyT_doubleton [lemma, in set3]
Bunion.partial_fun_axioms [definition, in set3]
Bunion.partial_fun_axioms_pr [lemma, in set3]
Bunion.partion_union_disjoint [lemma, in set3]
Bunion.partition [definition, in set3]
Bunion.partitionset_pr [lemma, in set3]
Bunion.partitions_is_covering [lemma, in set3]
Bunion.partition_fam [definition, in set3]
Bunion.partition_fam_is_covering [lemma, in set3]
Bunion.partition_fam_partition [lemma, in set3]
Bunion.partition_inc_exists [lemma, in set3]
Bunion.partition_inc_unique [lemma, in set3]
Bunion.partition_largest [lemma, in set3]
Bunion.partition_s [definition, in set3]
Bunion.partition_same [lemma, in set3]
Bunion.partition_same2 [lemma, in set3]
Bunion.partition_smallest [lemma, in set3]
Bunion.partition_with_complement [definition, in set3]
Bunion.powerset_emptyset [lemma, in set3]
Bunion.powerset_monotone [lemma, in set3]
Bunion.product_is_covering2 [lemma, in set3]
Bunion.product_of_covering [lemma, in set3]
Bunion.second_partial_fun [definition, in set3]
Bunion.second_partial_function [definition, in set3]
Bunion.second_partial_map [definition, in set3]
Bunion.set_extens_aux [lemma, in set3]
Bunion.set_of_functions [definition, in set3]
Bunion.set_of_functions_equipotent [lemma, in set3]
Bunion.set_of_functions_extens [lemma, in set3]
Bunion.set_of_functions_rw [lemma, in set3]
Bunion.set_of_gfunctions [definition, in set3]
Bunion.set_of_gfunctions_inc [lemma, in set3]
Bunion.set_of_permutations [definition, in set3]
Bunion.set_of_sub_functions [definition, in set3]
Bunion.set_of_sub_functions_rw [lemma, in set3]
Bunion.singleton_type_inj [lemma, in set3]
Bunion.smallest_partition [definition, in set3]
Bunion.small_set_of_functions_source [lemma, in set3]
Bunion.small_set_of_functions_target [lemma, in set3]
Bunion.spfa_axioms [lemma, in set3]
Bunion.spfa_bijective [lemma, in set3]
Bunion.spfa_function [lemma, in set3]
Bunion.spfa_W [lemma, in set3]
Bunion.spfb_axioms [lemma, in set3]
Bunion.spfb_function [lemma, in set3]
Bunion.spfb_W [lemma, in set3]
Bunion.spfb_WW [lemma, in set3]
Bunion.spf_axioms [lemma, in set3]
Bunion.spf_function [lemma, in set3]
Bunion.spf_W [lemma, in set3]
Bunion.sub_covering [lemma, in set3]
Bunion.sub_intersectiont [lemma, in set3]
Bunion.sub_uniont [lemma, in set3]
Bunion.sub_uniont2 [lemma, in set3]
Bunion.Uintegral [inductive, in set3]
Bunion.unionb [definition, in set3]
Bunion.unionb_alt [lemma, in set3]
Bunion.unionb_exists [lemma, in set3]
Bunion.unionb_extensionality [lemma, in set3]
Bunion.unionb_identity [lemma, in set3]
Bunion.unionb_inc [lemma, in set3]
Bunion.unionb_rewrite [lemma, in set3]
Bunion.unionb_rewrite1 [lemma, in set3]
Bunion.unionb_rw [lemma, in set3]
Bunion.unionf [definition, in set3]
Bunion.unionf_exists [lemma, in set3]
Bunion.unionf_extensionality [lemma, in set3]
Bunion.unionf_inc [lemma, in set3]
Bunion.unionf_rw [lemma, in set3]
Bunion.unionf_singleton [lemma, in set3]
Bunion.uniont [definition, in set3]
Bunion.uniont_constant [lemma, in set3]
Bunion.uniont_constant_alt [lemma, in set3]
Bunion.uniont_exists [lemma, in set3]
Bunion.uniont_extensionality [lemma, in set3]
Bunion.uniont_inc [lemma, in set3]
Bunion.uniont_rewrite [lemma, in set3]
Bunion.uniont_rw [lemma, in set3]
Bunion.uniont_singleton [lemma, in set3]
Bunion.uniont_sub [lemma, in set3]
Bunion.union2assoc [lemma, in set3]
Bunion.union2_comp [lemma, in set3]
Bunion.union2_complement [lemma, in set3]
Bunion.union_assoc [lemma, in set3]
Bunion.union_doubleton [lemma, in set3]
Bunion.union_monotone [lemma, in set3]
Bunion.union_monotone2 [lemma, in set3]
Bunion.union_of_twosets [lemma, in set3]
Bunion.union_of_twosets_aux [lemma, in set3]
Bunion.union_prop [lemma, in set3]
Bunion.union_singleton [lemma, in set3]
Bunion.variant [definition, in set3]
Bunion.variantL [definition, in set3]
Bunion.variantLc [definition, in set3]
Bunion.variantLc_domain [lemma, in set3]
Bunion.variantLc_domain_nonempty [lemma, in set3]
Bunion.variantLc_fgraph [lemma, in set3]
Bunion.variant_domain [lemma, in set3]
Bunion.variant_fgraph [lemma, in set3]
Bunion.variant_if_not_rw [lemma, in set3]
Bunion.variant_if_rw [lemma, in set3]
Bunion.variant_V_a [lemma, in set3]
Bunion.variant_V_b [lemma, in set3]
Bunion.variant_V_ca [lemma, in set3]
Bunion.variant_V_cb [lemma, in set3]
C
Cardinal [module, in set7]Cardinal.cantor [lemma, in set7]
Cardinal.cantor_bis [lemma, in set7]
Cardinal.cardinal [definition, in set7]
Cardinal.cardinal0 [lemma, in set7]
Cardinal.cardinal1 [lemma, in set7]
Cardinal.cardinal2 [lemma, in set7]
Cardinal.cardinal_antisymmetry1 [lemma, in set7]
Cardinal.cardinal_antisymmetry2 [lemma, in set7]
Cardinal.cardinal_cardinal [lemma, in set7]
Cardinal.cardinal_distrib_prod2_sum [lemma, in set7]
Cardinal.cardinal_distrib_prod_sum [lemma, in set7]
Cardinal.cardinal_distrib_prod_sum2 [lemma, in set7]
Cardinal.cardinal_distrib_prod_sum3 [lemma, in set7]
Cardinal.cardinal_doubleton [lemma, in set7]
Cardinal.cardinal_emptyset [lemma, in set7]
Cardinal.cardinal_equipotent [lemma, in set7]
Cardinal.cardinal_equipotent1 [lemma, in set7]
Cardinal.cardinal_le [definition, in set7]
Cardinal.cardinal_le1 [lemma, in set7]
Cardinal.cardinal_le2 [lemma, in set7]
Cardinal.cardinal_le3 [lemma, in set7]
Cardinal.cardinal_le5 [lemma, in set7]
Cardinal.cardinal_le7 [lemma, in set7]
Cardinal.cardinal_le8 [lemma, in set7]
Cardinal.cardinal_le9 [lemma, in set7]
Cardinal.cardinal_le_lt_trans [lemma, in set7]
Cardinal.cardinal_le_reflexive [lemma, in set7]
Cardinal.cardinal_le_total_order [lemma, in set7]
Cardinal.cardinal_le_total_order1 [lemma, in set7]
Cardinal.cardinal_le_total_order2 [lemma, in set7]
Cardinal.cardinal_le_total_order3 [lemma, in set7]
Cardinal.cardinal_le_transitive [lemma, in set7]
Cardinal.cardinal_le_when_complement [lemma, in set7]
Cardinal.cardinal_lt [definition, in set7]
Cardinal.cardinal_lt_le_trans [lemma, in set7]
Cardinal.cardinal_nonemptyset [lemma, in set7]
Cardinal.cardinal_nonemptyset1 [lemma, in set7]
Cardinal.cardinal_of_cardinal [lemma, in set7]
Cardinal.cardinal_one_is_singleton [lemma, in set7]
Cardinal.cardinal_pr [lemma, in set7]
Cardinal.cardinal_prod [definition, in set7]
Cardinal.cardinal_prod_assoc [lemma, in set7]
Cardinal.cardinal_prod_commutative [lemma, in set7]
Cardinal.cardinal_prod_pr [lemma, in set7]
Cardinal.cardinal_pr0 [lemma, in set7]
Cardinal.cardinal_singleton [lemma, in set7]
Cardinal.cardinal_sum [definition, in set7]
Cardinal.cardinal_sum_assoc [lemma, in set7]
Cardinal.cardinal_sum_commutative [lemma, in set7]
Cardinal.cardinal_sum_pr [lemma, in set7]
Cardinal.cardinal_sum_pr1 [lemma, in set7]
Cardinal.cardinal_sum_pr2 [lemma, in set7]
Cardinal.cardinal_sum_pr3 [lemma, in set7]
Cardinal.cardinal_supremum [lemma, in set7]
Cardinal.cardinal_supremum1 [lemma, in set7]
Cardinal.cardinal_two_is_doubleton [lemma, in set7]
Cardinal.cardinal_zero [lemma, in set7]
Cardinal.card_commutative_aux [lemma, in set7]
Cardinal.card_le_one_prop [lemma, in set7]
Cardinal.card_le_one_prop1 [lemma, in set7]
Cardinal.card_le_two_prop [lemma, in set7]
Cardinal.card_le_two_prop1 [lemma, in set7]
Cardinal.card_mult [definition, in set7]
Cardinal.card_mult_associative [lemma, in set7]
Cardinal.card_mult_commutative [lemma, in set7]
Cardinal.card_mult_is_cardinal [lemma, in set7]
Cardinal.card_mult_pr [lemma, in set7]
Cardinal.card_mult_pr0 [lemma, in set7]
Cardinal.card_mult_pr1 [lemma, in set7]
Cardinal.card_mult_pr2 [lemma, in set7]
Cardinal.card_one [definition, in set7]
Cardinal.card_one_not_two [lemma, in set7]
Cardinal.card_one_not_zero [lemma, in set7]
Cardinal.card_plus [definition, in set7]
Cardinal.card_plus_associative [lemma, in set7]
Cardinal.card_plus_commutative [lemma, in set7]
Cardinal.card_plus_is_cardinal [lemma, in set7]
Cardinal.card_plus_pr [lemma, in set7]
Cardinal.card_plus_pr0 [lemma, in set7]
Cardinal.card_plus_pr1 [lemma, in set7]
Cardinal.card_plus_pr2 [lemma, in set7]
Cardinal.card_pow [definition, in set7]
Cardinal.card_powerset [lemma, in set7]
Cardinal.card_pow_pr [lemma, in set7]
Cardinal.card_pow_pr1 [lemma, in set7]
Cardinal.card_pow_pr2 [lemma, in set7]
Cardinal.card_pow_pr3 [lemma, in set7]
Cardinal.card_two [definition, in set7]
Cardinal.card_two_not_zero [lemma, in set7]
Cardinal.card_two_pr [lemma, in set7]
Cardinal.card_zero [definition, in set7]
Cardinal.disjoint_union2_pr [lemma, in set7]
Cardinal.disjoint_union2_pr0 [lemma, in set7]
Cardinal.disjoint_union2_pr1 [lemma, in set7]
Cardinal.disjoint_union2_pr3 [lemma, in set7]
Cardinal.disjoint_union2_pr4 [lemma, in set7]
Cardinal.disjoint_with_singleton [lemma, in set7]
Cardinal.distrib_inter_prod2 [lemma, in set7]
Cardinal.distrib_inter_prod3 [lemma, in set7]
Cardinal.distrib_prod2_sum [lemma, in set7]
Cardinal.doubleton_equipotent1 [lemma, in set7]
Cardinal.doubleton_fam [definition, in set7]
Cardinal.doubleton_fam_canon [lemma, in set7]
Cardinal.equipotent_a_times_singl [lemma, in set7]
Cardinal.equipotent_disjoint_union [lemma, in set7]
Cardinal.equipotent_disjoint_union1 [lemma, in set7]
Cardinal.equipotent_disjoint_union2 [lemma, in set7]
Cardinal.equipotent_product [lemma, in set7]
Cardinal.equipotent_productb [lemma, in set7]
Cardinal.equipotent_productf [lemma, in set7]
Cardinal.equipotent_product1 [lemma, in set7]
Cardinal.equipotent_product_sym [lemma, in set7]
Cardinal.equipotent_singl_times_a [lemma, in set7]
Cardinal.equipotent_to_emptyset [lemma, in set7]
Cardinal.equipotent_to_subset [definition, in set7]
Cardinal.image_smaller_cardinal [lemma, in set7]
Cardinal.inj_compose1 [lemma, in set7]
Cardinal.is_cardinal [definition, in set7]
Cardinal.nonempty_card_ge2 [lemma, in set7]
Cardinal.not_card_le_lt [lemma, in set7]
Cardinal.one_small_cardinal [lemma, in set7]
Cardinal.one_small_cardinal1 [lemma, in set7]
Cardinal.one_unit_prod [lemma, in set7]
Cardinal.one_unit_prodl [lemma, in set7]
Cardinal.one_unit_prodr [lemma, in set7]
Cardinal.power_increasing1 [lemma, in set7]
Cardinal.power_of_prod [lemma, in set7]
Cardinal.power_of_prod2 [lemma, in set7]
Cardinal.power_of_prod3 [lemma, in set7]
Cardinal.power_of_sum [lemma, in set7]
Cardinal.power_of_sum2 [lemma, in set7]
Cardinal.power_x_0 [lemma, in set7]
Cardinal.power_x_1 [lemma, in set7]
Cardinal.power_x_2 [lemma, in set7]
Cardinal.power_0_x [lemma, in set7]
Cardinal.power_0_0 [lemma, in set7]
Cardinal.power_1_x [lemma, in set7]
Cardinal.product2associative [lemma, in set7]
Cardinal.product_increasing [lemma, in set7]
Cardinal.product_increasing1 [lemma, in set7]
Cardinal.product_increasing2 [lemma, in set7]
Cardinal.product_increasing3 [lemma, in set7]
Cardinal.restriction_to_image [definition, in set7]
Cardinal.restriction_to_image_axioms [lemma, in set7]
Cardinal.restriction_to_image_bijective [lemma, in set7]
Cardinal.restriction_to_image_surjective [lemma, in set7]
Cardinal.set_of_cardinals_le [definition, in set7]
Cardinal.set_of_cardinals_pr [lemma, in set7]
Cardinal.set_of_card_two [lemma, in set7]
Cardinal.singletons_equipotent [lemma, in set7]
Cardinal.sub_smaller [lemma, in set7]
Cardinal.succ_injective [lemma, in set7]
Cardinal.sum_increasing [lemma, in set7]
Cardinal.sum_increasing1 [lemma, in set7]
Cardinal.sum_increasing2 [lemma, in set7]
Cardinal.sum_increasing3 [lemma, in set7]
Cardinal.sum_of_ones [lemma, in set7]
Cardinal.sum_of_ones1 [lemma, in set7]
Cardinal.sum_of_same [lemma, in set7]
Cardinal.sum_of_same1 [lemma, in set7]
Cardinal.surjective_cardinal_le [lemma, in set7]
Cardinal.TPas [definition, in set7]
Cardinal.TPbs [definition, in set7]
Cardinal.trivial_cardinal_prod [lemma, in set7]
Cardinal.trivial_cardinal_prod1 [lemma, in set7]
Cardinal.trivial_cardinal_sum [lemma, in set7]
Cardinal.trivial_cardinal_sum1 [lemma, in set7]
Cardinal.trivial_card_plus [lemma, in set7]
Cardinal.two_terms_bij [lemma, in set7]
Cardinal.wordering_cardinal_le [lemma, in set7]
Cardinal.wordering_cardinal_le_pr [lemma, in set7]
Cardinal.zero_cardinal_product [lemma, in set7]
Cardinal.zero_cardinal_product2 [lemma, in set7]
Cardinal.zero_is_emptyset [lemma, in set7]
Cardinal.zero_product_absorbing [lemma, in set7]
Cardinal.zero_prod_absorbing [lemma, in set7]
Cardinal.zero_smallest [lemma, in set7]
Cardinal.zero_smallest1 [lemma, in set7]
Cardinal.zero_smallest2 [lemma, in set7]
Cardinal.zero_unit_sum [lemma, in set7]
Cardinal.zero_unit_suml [lemma, in set7]
Cardinal.zero_unit_sumr [lemma, in set7]
Cartesian [module, in set1]
Cartesian.empty_product1 [lemma, in set1]
Cartesian.empty_product2 [lemma, in set1]
Cartesian.empty_product_pr [lemma, in set1]
Cartesian.pair_in_product [lemma, in set1]
Cartesian.product [definition, in set1]
Cartesian.product_inc [lemma, in set1]
Cartesian.product_inc_rw [lemma, in set1]
Cartesian.product_monotone [lemma, in set1]
Cartesian.product_monotone_left [lemma, in set1]
Cartesian.product_monotone_left2 [lemma, in set1]
Cartesian.product_monotone_right [lemma, in set1]
Cartesian.product_monotone_right2 [lemma, in set1]
Cartesian.product_pair_inc [lemma, in set1]
Cartesian.product_pair_pr [lemma, in set1]
Cartesian.product_pr [lemma, in set1]
chooseT [axiom, in set1]
chooseT_pr [axiom, in set1]
Complement [module, in set1]
Complement.complement [definition, in set1]
Complement.complement_emptyset [lemma, in set1]
Complement.complement_itself [lemma, in set1]
Complement.complement_monotone [lemma, in set1]
Complement.double_complement [lemma, in set1]
Complement.empty_complement [lemma, in set1]
Complement.inc_complement [lemma, in set1]
Complement.not_inc_complement_singleton [lemma, in set1]
Complement.strict_sub_nonempty_complement [lemma, in set1]
Complement.sub_complement [lemma, in set1]
Complement.use_complement [lemma, in set1]
Constructions [module, in set1]
Constructions.arrow_EP_exten [lemma, in set1]
Constructions.Bo [definition, in set1]
Constructions.by_cases [definition, in set1]
Constructions.by_cases_if [lemma, in set1]
Constructions.by_cases_if_not [lemma, in set1]
Constructions.by_cases_nonempty [lemma, in set1]
Constructions.B_back [lemma, in set1]
Constructions.B_eq [lemma, in set1]
Constructions.choose [definition, in set1]
Constructions.choosenat [definition, in set1]
Constructions.choosenat_pr [lemma, in set1]
Constructions.choose_equiv [lemma, in set1]
Constructions.choose_not [lemma, in set1]
Constructions.choose_pr [lemma, in set1]
Constructions.cut [definition, in set1]
Constructions.cut_inc [lemma, in set1]
Constructions.cut_pr [lemma, in set1]
Constructions.cut_sub [lemma, in set1]
Constructions.cut_to [definition, in set1]
Constructions.cut_to_R_eq [lemma, in set1]
Constructions.empty [definition, in set1]
Constructions.emptyset [inductive, in set1]
Constructions.emptyset_dichot [lemma, in set1]
Constructions.emptyset_pr [lemma, in set1]
Constructions.emptyset_sub_any [lemma, in set1]
Constructions.exists_proof [lemma, in set1]
Constructions.exists_unique [definition, in set1]
Constructions.inc_nonempty [lemma, in set1]
Constructions.is_emptyset [lemma, in set1]
Constructions.nonemptyT_not_empty [lemma, in set1]
Constructions.nonemptyT_not_empty0 [lemma, in set1]
Constructions.nonempty_rep [lemma, in set1]
Constructions.not_empty_nonemptyT [lemma, in set1]
Constructions.not_exists_pr [lemma, in set1]
Constructions.rep [definition, in set1]
Constructions.R_inc [lemma, in set1]
Constructions.strict_sub [definition, in set1]
Constructions.strict_sub_trans1 [lemma, in set1]
Constructions.strict_sub_trans2 [lemma, in set1]
Constructions.sub_refl [lemma, in set1]
Constructions.sub_trans [lemma, in set1]
Constructions.Xo [definition, in set1]
Constructions.X_eq [lemma, in set1]
Constructions.X_rewrite [lemma, in set1]
Constructions.Yo [definition, in set1]
Constructions.Yt [definition, in set1]
Constructions.Yt_if_not_rw [lemma, in set1]
Constructions.Yt_if_rw [lemma, in set1]
Constructions.Yy [definition, in set1]
Constructions.Yy_if [lemma, in set1]
Constructions.Yy_if_not [lemma, in set1]
Constructions.Y_if [lemma, in set1]
Constructions.Y_if_not [lemma, in set1]
Constructions.Y_if_not_rw [lemma, in set1]
Constructions.Y_if_rw [lemma, in set1]
Constructions.Zo [definition, in set1]
Constructions.Zorec [inductive, in set1]
Constructions.Zorec_c [constructor, in set1]
Constructions.Z_all [lemma, in set1]
Constructions.Z_inc [lemma, in set1]
Constructions.Z_sub [lemma, in set1]
Correspondence [module, in set2]
Correspondence.acreate [definition, in set2]
Correspondence.acreate_corresp [lemma, in set2]
Correspondence.composableC [definition, in set2]
Correspondence.compose [definition, in set2]
Correspondence.compose_correspondence [lemma, in set2]
Correspondence.compose_domain [lemma, in set2]
Correspondence.compose_domain1 [lemma, in set2]
Correspondence.compose_graph [definition, in set2]
Correspondence.compose_identity_identity [lemma, in set2]
Correspondence.compose_identity_left [lemma, in set2]
Correspondence.compose_identity_right [lemma, in set2]
Correspondence.compose_of_sets [lemma, in set2]
Correspondence.compose_range [lemma, in set2]
Correspondence.compose_range1 [lemma, in set2]
Correspondence.compose_related [lemma, in set2]
Correspondence.composition_associative [lemma, in set2]
Correspondence.composition_increasing [lemma, in set2]
Correspondence.composition_is_graph [lemma, in set2]
Correspondence.constant_function_p1 [lemma, in set2]
Correspondence.corresp [definition, in set2]
Correspondence.corresp_create [lemma, in set2]
Correspondence.corresp_graph [lemma, in set2]
Correspondence.corresp_is_graph [lemma, in set2]
Correspondence.corresp_propb [lemma, in set2]
Correspondence.corresp_recov [lemma, in set2]
Correspondence.corresp_source [lemma, in set2]
Correspondence.corresp_sub_domain [lemma, in set2]
Correspondence.corresp_sub_range [lemma, in set2]
Correspondence.corresp_target [lemma, in set2]
Correspondence.corr_propa [lemma, in set2]
Correspondence.corr_propb [definition, in set2]
Correspondence.corr_propc [lemma, in set2]
Correspondence.diagonal [definition, in set2]
Correspondence.diagonal_is_identity [lemma, in set2]
Correspondence.domain_inverse [lemma, in set2]
Correspondence.emptyset_domain [lemma, in set2]
Correspondence.emptyset_fgraph [lemma, in set2]
Correspondence.emptyset_graph [lemma, in set2]
Correspondence.emptyset_range [lemma, in set2]
Correspondence.empty_graph1 [lemma, in set2]
Correspondence.empty_graph2 [lemma, in set2]
Correspondence.gacreate [definition, in set2]
Correspondence.graph [definition, in set2]
Correspondence.identity [definition, in set2]
Correspondence.identity_corresp [lemma, in set2]
Correspondence.identity_graph [lemma, in set2]
Correspondence.identity_range [lemma, in set2]
Correspondence.identity_self_inverse [lemma, in set2]
Correspondence.identity_source [lemma, in set2]
Correspondence.identity_target [lemma, in set2]
Correspondence.image_by_emptyset [lemma, in set2]
Correspondence.image_by_fun [definition, in set2]
Correspondence.image_by_graph [definition, in set2]
Correspondence.image_by_graph_domain [lemma, in set2]
Correspondence.image_by_graph_rw [lemma, in set2]
Correspondence.image_by_increasing [lemma, in set2]
Correspondence.image_by_nonemptyset [lemma, in set2]
Correspondence.image_composition [lemma, in set2]
Correspondence.image_of_fun [definition, in set2]
Correspondence.image_of_large [lemma, in set2]
Correspondence.im_singleton [definition, in set2]
Correspondence.im_singleton_inclusion [lemma, in set2]
Correspondence.im_singleton_pr [lemma, in set2]
Correspondence.inc_compose [lemma, in set2]
Correspondence.inc_diagonal_rw [lemma, in set2]
Correspondence.inc_pair_diagonal [lemma, in set2]
Correspondence.inverse_compose [lemma, in set2]
Correspondence.inverse_compose_cor [lemma, in set2]
Correspondence.inverse_correspondence [lemma, in set2]
Correspondence.inverse_direct_image [lemma, in set2]
Correspondence.inverse_fun [definition, in set2]
Correspondence.inverse_fun_involutive [lemma, in set2]
Correspondence.inverse_graph [definition, in set2]
Correspondence.inverse_graph_alt [lemma, in set2]
Correspondence.inverse_graph_emptyset [lemma, in set2]
Correspondence.inverse_graph_involutive [lemma, in set2]
Correspondence.inverse_graph_is_graph [lemma, in set2]
Correspondence.inverse_graph_pair [lemma, in set2]
Correspondence.inverse_graph_pr2 [lemma, in set2]
Correspondence.inverse_graph_rw [lemma, in set2]
Correspondence.inverse_identity_g [lemma, in set2]
Correspondence.inverse_product [lemma, in set2]
Correspondence.inverse_source [lemma, in set2]
Correspondence.inverse_target [lemma, in set2]
Correspondence.inv_image_by_fun [definition, in set2]
Correspondence.inv_image_by_fun_pr [lemma, in set2]
Correspondence.inv_image_by_graph [definition, in set2]
Correspondence.inv_image_graph_rw [lemma, in set2]
Correspondence.is_correspondence [definition, in set2]
Correspondence.is_triple [definition, in set2]
Correspondence.is_triple_corr [lemma, in set2]
Correspondence.product_domain [lemma, in set2]
Correspondence.product_is_graph [lemma, in set2]
Correspondence.product_range [lemma, in set2]
Correspondence.product_related [lemma, in set2]
Correspondence.range_domain_exists [lemma, in set2]
Correspondence.range_inverse [lemma, in set2]
Correspondence.related [definition, in set2]
Correspondence.set_of_correspondences [definition, in set2]
Correspondence.set_of_correspondences_propa [lemma, in set2]
Correspondence.set_of_correspondences_rw [lemma, in set2]
Correspondence.source [definition, in set2]
Correspondence.sub_emptyset [lemma, in set2]
Correspondence.sub_graph_prod [lemma, in set2]
Correspondence.sub_image_by_graph [lemma, in set2]
Correspondence.target [definition, in set2]
E
excluded_middle [axiom, in set1]extensionality [axiom, in set1]
F
FiniteSets [module, in set8]FiniteSets.bijective_if_same_finite_c_inj [lemma, in set8]
FiniteSets.bijective_if_same_finite_c_surj [lemma, in set8]
FiniteSets.Bnat [definition, in set8]
FiniteSets.Bnat_interval_cc_pr [lemma, in set8]
FiniteSets.Bnat_interval_cc_pr1 [lemma, in set8]
FiniteSets.Bnat_interval_co_pr [lemma, in set8]
FiniteSets.Bnat_interval_co_pr1 [lemma, in set8]
FiniteSets.Bnat_is_cardinal [lemma, in set8]
FiniteSets.Bnat_le [definition, in set8]
FiniteSets.Bnat_lt [definition, in set8]
FiniteSets.Bnat_order [definition, in set8]
FiniteSets.Bnat_order_le [lemma, in set8]
FiniteSets.Bnat_order_substrate [lemma, in set8]
FiniteSets.Bnat_order_worder [lemma, in set8]
FiniteSets.Bnat_stable_mult [lemma, in set8]
FiniteSets.Bnat_stable_plus [lemma, in set8]
FiniteSets.Bnat_wordered [lemma, in set8]
FiniteSets.cardinal_c_induction [lemma, in set8]
FiniteSets.cardinal_c_induction1 [lemma, in set8]
FiniteSets.cardinal_c_induction2 [lemma, in set8]
FiniteSets.cardinal_c_induction3 [lemma, in set8]
FiniteSets.cardinal_c_induction3_v [lemma, in set8]
FiniteSets.cardinal_c_induction4 [lemma, in set8]
FiniteSets.cardinal_c_induction4_v [lemma, in set8]
FiniteSets.cardinal_c_induction_v [lemma, in set8]
FiniteSets.cardinal_le_when_complement1 [lemma, in set8]
FiniteSets.cardinal_nat [definition, in set8]
FiniteSets.cardinal_nat_cardinal [lemma, in set8]
FiniteSets.cardinal_nat_doubleton [lemma, in set8]
FiniteSets.cardinal_nat_emptyset [lemma, in set8]
FiniteSets.cardinal_nat_finite_eq [lemma, in set8]
FiniteSets.cardinal_nat_finite_eq1 [lemma, in set8]
FiniteSets.cardinal_nat_one [lemma, in set8]
FiniteSets.cardinal_nat_pr [lemma, in set8]
FiniteSets.cardinal_nat_pr1 [lemma, in set8]
FiniteSets.cardinal_nat_singleton [lemma, in set8]
FiniteSets.cardinal_nat_two [lemma, in set8]
FiniteSets.cardinal_nat_zero [lemma, in set8]
FiniteSets.cardinal_Rnat_inj [lemma, in set8]
FiniteSets.cardinal_Rnat_lt [lemma, in set8]
FiniteSets.cardinal_succ [lemma, in set8]
FiniteSets.cardinal_succ_pr [lemma, in set8]
FiniteSets.cardinal_succ_pr0 [lemma, in set8]
FiniteSets.cardinal_succ_pr1 [lemma, in set8]
FiniteSets.card_four [definition, in set8]
FiniteSets.card_three [definition, in set8]
FiniteSets.decent_set [definition, in set8]
FiniteSets.doubleton_finite [lemma, in set8]
FiniteSets.emptyset_finite [lemma, in set8]
FiniteSets.exists_nat_cardinal [lemma, in set8]
FiniteSets.exists_predc [lemma, in set8]
FiniteSets.finite_domain_graph [lemma, in set8]
FiniteSets.finite_fun_image [lemma, in set8]
FiniteSets.finite_graph_domain [lemma, in set8]
FiniteSets.finite_graph_range [lemma, in set8]
FiniteSets.finite_image [lemma, in set8]
FiniteSets.finite_image_by [lemma, in set8]
FiniteSets.finite_in_product [lemma, in set8]
FiniteSets.finite_le_infinite [lemma, in set8]
FiniteSets.finite_lt_infinite [lemma, in set8]
FiniteSets.finite_powerset [lemma, in set8]
FiniteSets.finite_range [lemma, in set8]
FiniteSets.finite_Rnat [lemma, in set8]
FiniteSets.finite_set_induction [lemma, in set8]
FiniteSets.finite_set_induction0 [lemma, in set8]
FiniteSets.finite_set_induction1 [lemma, in set8]
FiniteSets.finite_set_induction2 [lemma, in set8]
FiniteSets.finite_set_induction3 [lemma, in set8]
FiniteSets.finite_set_maximal [lemma, in set8]
FiniteSets.finite_set_torder_greatest [lemma, in set8]
FiniteSets.finite_set_torder_worder [lemma, in set8]
FiniteSets.finite_subset_directed_bounded [lemma, in set8]
FiniteSets.finite_subset_lattice_inf [lemma, in set8]
FiniteSets.finite_subset_lattice_sup [lemma, in set8]
FiniteSets.finite_subset_torder_greatest [lemma, in set8]
FiniteSets.finite_subset_torder_least [lemma, in set8]
FiniteSets.finite_union2 [lemma, in set8]
FiniteSets.inc0_Bnat [lemma, in set8]
FiniteSets.inc1_Bnat [lemma, in set8]
FiniteSets.inc2_Bnat [lemma, in set8]
FiniteSets.inc_Bnat [lemma, in set8]
FiniteSets.inc_Bnat_prop [lemma, in set8]
FiniteSets.inc_nat_to_B [lemma, in set8]
FiniteSets.inc_pseudo_pseudo [lemma, in set8]
FiniteSets.inc_succ_Bnat [lemma, in set8]
FiniteSets.infinite_set [definition, in set8]
FiniteSets.integer_is_cardinal [lemma, in set8]
FiniteSets.intersection_of_pseudo_ordinals [lemma, in set8]
FiniteSets.is_finite0 [lemma, in set8]
FiniteSets.is_finite1 [lemma, in set8]
FiniteSets.is_finite2 [lemma, in set8]
FiniteSets.is_finite3 [lemma, in set8]
FiniteSets.is_finite4 [lemma, in set8]
FiniteSets.is_finite_c [definition, in set8]
FiniteSets.is_finite_in_sum [lemma, in set8]
FiniteSets.is_finite_in_sum2 [lemma, in set8]
FiniteSets.is_finite_set [definition, in set8]
FiniteSets.is_finite_succ [lemma, in set8]
FiniteSets.is_finite_succ1 [lemma, in set8]
FiniteSets.is_finite_succ2 [lemma, in set8]
FiniteSets.is_infinite_c [definition, in set8]
FiniteSets.is_less_than_succ [lemma, in set8]
FiniteSets.is_lt_succ [lemma, in set8]
FiniteSets.le_int_in_Bnat [lemma, in set8]
FiniteSets.le_int_is_int [lemma, in set8]
FiniteSets.lt_is_le_succ [lemma, in set8]
FiniteSets.lt_is_le_succ1 [lemma, in set8]
FiniteSets.lt_n_succ_le0 [lemma, in set8]
FiniteSets.lt_n_succ_le1 [lemma, in set8]
FiniteSets.maximal_inclusion [lemma, in set8]
FiniteSets.mult_via_plus [lemma, in set8]
FiniteSets.natR [definition, in set8]
FiniteSets.nat_B_inj [lemma, in set8]
FiniteSets.nat_B_le [lemma, in set8]
FiniteSets.nat_B_lt [lemma, in set8]
FiniteSets.nat_B_lt0 [lemma, in set8]
FiniteSets.nat_B_lt1 [lemma, in set8]
FiniteSets.nat_B_mult [lemma, in set8]
FiniteSets.nat_B_plus [lemma, in set8]
FiniteSets.nat_B_S [lemma, in set8]
FiniteSets.nat_B_0 [lemma, in set8]
FiniteSets.nat_B_1 [lemma, in set8]
FiniteSets.nat_B_2 [lemma, in set8]
FiniteSets.nat_infinite_set [lemma, in set8]
FiniteSets.nat_to_B [definition, in set8]
FiniteSets.nat_to_B_pr [lemma, in set8]
FiniteSets.nat_to_B_pr1 [lemma, in set8]
FiniteSets.nat_to_B_surjective [lemma, in set8]
FiniteSets.of_finite_character [definition, in set8]
FiniteSets.of_finite_character_example [lemma, in set8]
FiniteSets.plus_via_succ [lemma, in set8]
FiniteSets.pow [definition, in set8]
FiniteSets.predc [definition, in set8]
FiniteSets.predc_pr [lemma, in set8]
FiniteSets.predc_pr0 [lemma, in set8]
FiniteSets.predc_pr1 [lemma, in set8]
FiniteSets.predc_pr2 [lemma, in set8]
FiniteSets.predc_pr3 [lemma, in set8]
FiniteSets.pseudo_not_inc_itself [lemma, in set8]
FiniteSets.pseudo_ordinal [definition, in set8]
FiniteSets.pseudo_ordinal_dichotomy [lemma, in set8]
FiniteSets.pseudo_ordinal_empty [lemma, in set8]
FiniteSets.pseudo_ordinal_emptyset [lemma, in set8]
FiniteSets.pseudo_ordinal_isomorphism_exists [lemma, in set8]
FiniteSets.pseudo_ordinal_isomorphism_unique [lemma, in set8]
FiniteSets.pseudo_ordinal_pr [lemma, in set8]
FiniteSets.pseudo_ordinal_pr1 [lemma, in set8]
FiniteSets.pseudo_ordinal_Rnat [lemma, in set8]
FiniteSets.pseudo_ordinal_tack_on [lemma, in set8]
FiniteSets.pseudo_ordinal_transitive [lemma, in set8]
FiniteSets.pseudo_ordinal_transitive1 [lemma, in set8]
FiniteSets.Rnat_inc_lt [lemma, in set8]
FiniteSets.Rnat_le_implies_sub [lemma, in set8]
FiniteSets.Rnat_lt_implies_inc [lemma, in set8]
FiniteSets.Rnat_lt_implies_strict_sub [lemma, in set8]
FiniteSets.Rnat_sub_le [lemma, in set8]
FiniteSets.Rnot_inc_itself [lemma, in set8]
FiniteSets.set_of_finite_subsets [definition, in set8]
FiniteSets.set_of_finite_subsets_pr [lemma, in set8]
FiniteSets.set_of_finite_subsets_prop [definition, in set8]
FiniteSets.singleton_finite [lemma, in set8]
FiniteSets.strict_sub_smaller [lemma, in set8]
FiniteSets.strict_sub_smaller1 [lemma, in set8]
FiniteSets.sub_finite_set [lemma, in set8]
FiniteSets.sub_image_of_fun [lemma, in set8]
FiniteSets.succ [definition, in set8]
FiniteSets.succ_cardinal [lemma, in set8]
FiniteSets.succ_is_cardinal [lemma, in set8]
FiniteSets.succ_nonzero [lemma, in set8]
FiniteSets.succ_nonzero1 [lemma, in set8]
FiniteSets.succ_positive [lemma, in set8]
FiniteSets.succ_zero [lemma, in set8]
FiniteSets.S_inj_not_bij [lemma, in set8]
FiniteSets.tack_if_succ_card [lemma, in set8]
FiniteSets.tack_on_finite [lemma, in set8]
FiniteSets.transitive_intersection [lemma, in set8]
FiniteSets.transitive_set [definition, in set8]
FiniteSets.transitive_tack_on_itself [lemma, in set8]
FiniteSets.transitive_union [lemma, in set8]
FiniteSets.value_R_0 [lemma, in set8]
FiniteSets.value_R_1 [lemma, in set8]
FiniteSets.value_R_2 [lemma, in set8]
FiniteSets.value_R_3 [lemma, in set8]
FiniteSets.worder_sub_ordinal [lemma, in set8]
FiniteSets.zero_lt_one [lemma, in set8]
Function [module, in set1]
Function.alternate_compose [lemma, in set1]
Function.domain [definition, in set1]
Function.domain_rw [lemma, in set1]
Function.domain_union [lemma, in set1]
Function.domain_union2 [lemma, in set1]
Function.double_restr [lemma, in set1]
Function.fcomposable [definition, in set1]
Function.fcomposable_domain [lemma, in set1]
Function.fcompose [definition, in set1]
Function.fcompose_domain [lemma, in set1]
Function.fcompose_ev [lemma, in set1]
Function.fcompose_ev1 [lemma, in set1]
Function.fcompose_fgraph [lemma, in set1]
Function.fcompose_range [lemma, in set1]
Function.fdomain_pr1 [lemma, in set1]
Function.fgraph [definition, in set1]
Function.fgraph_exten [lemma, in set1]
Function.fgraph_is_graph [lemma, in set1]
Function.fgraph_pr [lemma, in set1]
Function.fgraph_sub [lemma, in set1]
Function.fgraph_sub_eq [lemma, in set1]
Function.fgraph_sub_V [lemma, in set1]
Function.fgraph_union2 [lemma, in set1]
Function.frange_inc_rw [lemma, in set1]
Function.gcompose [definition, in set1]
Function.graph_constructor [definition, in set1]
Function.identity_domain [lemma, in set1]
Function.identity_ev [lemma, in set1]
Function.identity_fgraph [lemma, in set1]
Function.identity_g [definition, in set1]
Function.inc_pr1_domain [lemma, in set1]
Function.inc_pr2_range [lemma, in set1]
Function.inc_V_range [lemma, in set1]
Function.inverse_image [definition, in set1]
Function.inverse_image_inc [lemma, in set1]
Function.inverse_image_pr [lemma, in set1]
Function.inverse_image_sub [lemma, in set1]
Function.in_graph_V [lemma, in set1]
Function.is_graph [definition, in set1]
Function.is_restriction [definition, in set1]
Function.is_restriction_pr [lemma, in set1]
Function.L_create [lemma, in set1]
Function.L_domain [lemma, in set1]
Function.L_exten1 [lemma, in set1]
Function.L_fgraph [lemma, in set1]
Function.L_range [lemma, in set1]
Function.L_range_rw [lemma, in set1]
Function.L_recovers [lemma, in set1]
Function.L_V_out [lemma, in set1]
Function.L_V_rewrite [lemma, in set1]
Function.pr2_V [lemma, in set1]
Function.range [definition, in set1]
Function.range_rw [lemma, in set1]
Function.range_union [lemma, in set1]
Function.range_union2 [lemma, in set1]
Function.restr [definition, in set1]
Function.restr_domain [lemma, in set1]
Function.restr_domain1 [lemma, in set1]
Function.restr_ev [lemma, in set1]
Function.restr_ev1 [lemma, in set1]
Function.restr_fgraph [lemma, in set1]
Function.restr_graph [lemma, in set1]
Function.restr_inc_rw [lemma, in set1]
Function.restr_sub [lemma, in set1]
Function.restr_to_domain [lemma, in set1]
Function.restr_to_domain2 [lemma, in set1]
Function.sub_graph_domain [lemma, in set1]
Function.sub_graph_ev [lemma, in set1]
Function.sub_graph_fgraph [lemma, in set1]
Function.sub_graph_range [lemma, in set1]
Function.tack_on_domain [lemma, in set1]
Function.tack_on_fgraph [lemma, in set1]
Function.tack_on_range [lemma, in set1]
Function.tcreate [definition, in set1]
Function.tcreate_domain [lemma, in set1]
Function.tcreate_value_inc [lemma, in set1]
Function.tcreate_value_type [lemma, in set1]
I
iff_eq [axiom, in set1]IM [axiom, in set1]
Image [module, in set1]
Image.fun_image [definition, in set1]
Image.fun_image_rw [lemma, in set1]
Image.inc_fun_image [lemma, in set1]
IM_exists [axiom, in set1]
IM_inc [axiom, in set1]
InfiniteSets [module, in set10]
InfiniteSets.cardinal_comp_singl_inf [lemma, in set10]
InfiniteSets.countable_finite_or_N [lemma, in set10]
InfiniteSets.countable_finite_or_N_b [lemma, in set10]
InfiniteSets.countable_finite_or_N_c [lemma, in set10]
InfiniteSets.countable_inv_image [lemma, in set10]
InfiniteSets.countable_product [lemma, in set10]
InfiniteSets.countable_prop [lemma, in set10]
InfiniteSets.countable_subset [lemma, in set10]
InfiniteSets.countable_union [lemma, in set10]
InfiniteSets.decreasing_prop [lemma, in set10]
InfiniteSets.decreasing_sequence [definition, in set10]
InfiniteSets.decreasing_stationary [lemma, in set10]
InfiniteSets.equipotent_inf2_inf [lemma, in set10]
InfiniteSets.equipotent_nat_Bnat [lemma, in set10]
InfiniteSets.equipotent_N2_N [lemma, in set10]
InfiniteSets.equipotent_range [lemma, in set10]
InfiniteSets.finite_family_product [lemma, in set10]
InfiniteSets.finite_increasing_stationary [lemma, in set10]
InfiniteSets.increasing_prop [lemma, in set10]
InfiniteSets.increasing_sequence [definition, in set10]
InfiniteSets.increasing_stationary [lemma, in set10]
InfiniteSets.induction_defined [definition, in set10]
InfiniteSets.induction_defined0 [definition, in set10]
InfiniteSets.induction_defined0_set [definition, in set10]
InfiniteSets.induction_defined1 [definition, in set10]
InfiniteSets.induction_defined1_set [definition, in set10]
InfiniteSets.induction_defined_pr [lemma, in set10]
InfiniteSets.induction_defined_pr0 [lemma, in set10]
InfiniteSets.induction_defined_pr1 [lemma, in set10]
InfiniteSets.induction_defined_pr_set [lemma, in set10]
InfiniteSets.induction_defined_pr_set0 [lemma, in set10]
InfiniteSets.induction_defined_pr_set1 [lemma, in set10]
InfiniteSets.induction_defined_set [definition, in set10]
InfiniteSets.infinite_Bnat [lemma, in set10]
InfiniteSets.infinite_finite_sequence [lemma, in set10]
InfiniteSets.infinite_finite_subsets [lemma, in set10]
InfiniteSets.infinite_greater_countable [lemma, in set10]
InfiniteSets.infinite_greater_countable1 [lemma, in set10]
InfiniteSets.infinite_partition [lemma, in set10]
InfiniteSets.integer_induction [lemma, in set10]
InfiniteSets.integer_induction0 [lemma, in set10]
InfiniteSets.integer_induction1 [lemma, in set10]
InfiniteSets.integer_induction_stable [lemma, in set10]
InfiniteSets.integer_induction_stable0 [lemma, in set10]
InfiniteSets.integer_induction_stable1 [lemma, in set10]
InfiniteSets.is_countable_set [definition, in set10]
InfiniteSets.morphism_range [lemma, in set10]
InfiniteSets.morphism_range1 [lemma, in set10]
InfiniteSets.noetherian_induction [lemma, in set10]
InfiniteSets.notbig_family_sum [lemma, in set10]
InfiniteSets.notbig_family_sum1 [lemma, in set10]
InfiniteSets.power_of_infinite [lemma, in set10]
InfiniteSets.product2_infinite [lemma, in set10]
InfiniteSets.segment_Bnat_order [lemma, in set10]
InfiniteSets.stationary_sequence [definition, in set10]
InfiniteSets.sum2_infinite [lemma, in set10]
IntegerProps [module, in set9]
IntegerProps.app_nth3 [lemma, in set9]
IntegerProps.back_to_nat [definition, in set9]
IntegerProps.back_to_nat_pr [lemma, in set9]
IntegerProps.back_to_nat_pr1 [lemma, in set9]
IntegerProps.back_to_nat_pr2 [lemma, in set9]
IntegerProps.bijective_complement [lemma, in set9]
IntegerProps.binom [definition, in set9]
IntegerProps.binomial1 [lemma, in set9]
IntegerProps.binomial2 [lemma, in set9]
IntegerProps.binomial3 [lemma, in set9]
IntegerProps.binomial4 [lemma, in set9]
IntegerProps.binomial5 [lemma, in set9]
IntegerProps.binomial7 [lemma, in set9]
IntegerProps.binom0 [lemma, in set9]
IntegerProps.binom1 [lemma, in set9]
IntegerProps.binom2 [lemma, in set9]
IntegerProps.binom2a [lemma, in set9]
IntegerProps.binom_alt_pr [lemma, in set9]
IntegerProps.binom_monotone1 [lemma, in set9]
IntegerProps.binom_monotone2 [lemma, in set9]
IntegerProps.binom_nn [lemma, in set9]
IntegerProps.binom_pr [lemma, in set9]
IntegerProps.binom_pr0 [lemma, in set9]
IntegerProps.binom_pr1 [lemma, in set9]
IntegerProps.binom_pr2 [lemma, in set9]
IntegerProps.binom_pr3 [lemma, in set9]
IntegerProps.binom_symmetric [lemma, in set9]
IntegerProps.binom_2plus [lemma, in set9]
IntegerProps.binom_2plus0 [lemma, in set9]
IntegerProps.Bnat_divides [definition, in set9]
IntegerProps.Bnat_division [lemma, in set9]
IntegerProps.Bnat_infinite [lemma, in set9]
IntegerProps.Bnat_le_antisymmetric [lemma, in set9]
IntegerProps.Bnat_le_reflexive [lemma, in set9]
IntegerProps.Bnat_le_transitive [lemma, in set9]
IntegerProps.Bnat_mult_le_simplifiable [lemma, in set9]
IntegerProps.Bnat_mult_lt_simplifiable [lemma, in set9]
IntegerProps.Bnat_plus_le_simplifiable [lemma, in set9]
IntegerProps.Bnat_plus_lt_simplifiable [lemma, in set9]
IntegerProps.Bnat_stable_pow [lemma, in set9]
IntegerProps.Bnat_stable_sub [lemma, in set9]
IntegerProps.Bnat_total_order [lemma, in set9]
IntegerProps.Bnat_zero_smallest [lemma, in set9]
IntegerProps.Bnat_zero_smallest1 [lemma, in set9]
IntegerProps.b_power_k_large [lemma, in set9]
IntegerProps.cardinal_complement [lemma, in set9]
IntegerProps.cardinal_complement1 [lemma, in set9]
IntegerProps.cardinal_complement_image [lemma, in set9]
IntegerProps.cardinal_c_induction5_v [lemma, in set9]
IntegerProps.cardinal_interval [lemma, in set9]
IntegerProps.cardinal_interval0a [lemma, in set9]
IntegerProps.cardinal_interval1a [lemma, in set9]
IntegerProps.cardinal_interval_co_0a [lemma, in set9]
IntegerProps.cardinal_interval_co_0a1 [lemma, in set9]
IntegerProps.cardinal_le_a_apowb [lemma, in set9]
IntegerProps.cardinal_lt_pr [lemma, in set9]
IntegerProps.cardinal_pairs_le [lemma, in set9]
IntegerProps.cardinal_pairs_lt [lemma, in set9]
IntegerProps.cardinal_set_of_increasing_functions [lemma, in set9]
IntegerProps.cardinal_set_of_increasing_functions1 [lemma, in set9]
IntegerProps.cardinal_set_of_increasing_functions2 [lemma, in set9]
IntegerProps.cardinal_set_of_increasing_functions3 [lemma, in set9]
IntegerProps.cardinal_set_of_increasing_functions4 [lemma, in set9]
IntegerProps.card_interval_c0_pr [lemma, in set9]
IntegerProps.card_quo [definition, in set9]
IntegerProps.card_rem [definition, in set9]
IntegerProps.card_set_of_increasing_functions_int [lemma, in set9]
IntegerProps.card_sub [definition, in set9]
IntegerProps.card_sub0 [definition, in set9]
IntegerProps.card_sub_associative [lemma, in set9]
IntegerProps.card_sub_associativeN [lemma, in set9]
IntegerProps.card_sub_associative1 [lemma, in set9]
IntegerProps.card_sub_associative1N [lemma, in set9]
IntegerProps.card_sub_non_zero [lemma, in set9]
IntegerProps.card_sub_pr [lemma, in set9]
IntegerProps.card_sub_pr0 [lemma, in set9]
IntegerProps.card_sub_pr1 [lemma, in set9]
IntegerProps.card_sub_pr2 [lemma, in set9]
IntegerProps.card_sub_pr4 [lemma, in set9]
IntegerProps.card_sub_pr4N [lemma, in set9]
IntegerProps.card_sub_wrong [lemma, in set9]
IntegerProps.chart_fun_injective [lemma, in set9]
IntegerProps.char_fun [definition, in set9]
IntegerProps.char_fun_axioms [lemma, in set9]
IntegerProps.char_fun_complement [lemma, in set9]
IntegerProps.char_fun_constant [lemma, in set9]
IntegerProps.char_fun_function [lemma, in set9]
IntegerProps.char_fun_inter [lemma, in set9]
IntegerProps.char_fun_union [lemma, in set9]
IntegerProps.char_fun_W [lemma, in set9]
IntegerProps.char_fun_W_a [lemma, in set9]
IntegerProps.char_fun_W_aa [lemma, in set9]
IntegerProps.char_fun_W_b [lemma, in set9]
IntegerProps.char_fun_W_bb [lemma, in set9]
IntegerProps.char_fun_W_cardinal [lemma, in set9]
IntegerProps.contraction [definition, in set9]
IntegerProps.contraction_assoc [lemma, in set9]
IntegerProps.distrib_prod2_sub [lemma, in set9]
IntegerProps.distrib_prod2_subN [lemma, in set9]
IntegerProps.divides_and_difference [lemma, in set9]
IntegerProps.divides_and_sum [lemma, in set9]
IntegerProps.division_exists [lemma, in set9]
IntegerProps.division_prop [definition, in set9]
IntegerProps.division_prop_alt [lemma, in set9]
IntegerProps.division_prop_nat [lemma, in set9]
IntegerProps.division_result_integer [lemma, in set9]
IntegerProps.division_unique [lemma, in set9]
IntegerProps.domain_restr_empty [lemma, in set9]
IntegerProps.double_compl_ex [lemma, in set9]
IntegerProps.double_compl_nat [lemma, in set9]
IntegerProps.double_restrc [lemma, in set9]
IntegerProps.double_sub [lemma, in set9]
IntegerProps.double_subN [lemma, in set9]
IntegerProps.emptyset_interval_00 [lemma, in set9]
IntegerProps.equipotent_restriction [lemma, in set9]
IntegerProps.expansion_value [definition, in set9]
IntegerProps.factorial [definition, in set9]
IntegerProps.factorialC [definition, in set9]
IntegerProps.factorial0 [lemma, in set9]
IntegerProps.factorial1 [lemma, in set9]
IntegerProps.factorial2 [lemma, in set9]
IntegerProps.factorial_nonzero [lemma, in set9]
IntegerProps.factorial_prop [lemma, in set9]
IntegerProps.factorial_prop1 [lemma, in set9]
IntegerProps.factorial_succ [lemma, in set9]
IntegerProps.fct_prod [definition, in set9]
IntegerProps.fct_prod0 [lemma, in set9]
IntegerProps.fct_prod_const [lemma, in set9]
IntegerProps.fct_prod_mult [lemma, in set9]
IntegerProps.fct_prod_rec [lemma, in set9]
IntegerProps.fct_prod_rec1 [lemma, in set9]
IntegerProps.fct_prod_rev [lemma, in set9]
IntegerProps.fct_sum [definition, in set9]
IntegerProps.fct_sum0 [lemma, in set9]
IntegerProps.fct_sum_const [lemma, in set9]
IntegerProps.fct_sum_const1 [lemma, in set9]
IntegerProps.fct_sum_plus [lemma, in set9]
IntegerProps.fct_sum_rec [lemma, in set9]
IntegerProps.fct_sum_rec1 [lemma, in set9]
IntegerProps.fct_sum_rev [lemma, in set9]
IntegerProps.fct_to_list [definition, in set9]
IntegerProps.fct_to_listB [definition, in set9]
IntegerProps.fct_to_listB1 [definition, in set9]
IntegerProps.fct_to_listB_pr0 [lemma, in set9]
IntegerProps.fct_to_listB_pr1 [lemma, in set9]
IntegerProps.fct_to_listB_pr2 [lemma, in set9]
IntegerProps.fct_to_listB_pr3 [lemma, in set9]
IntegerProps.fct_to_list_length [lemma, in set9]
IntegerProps.fct_to_list_lengthB [lemma, in set9]
IntegerProps.fct_to_list_rev [definition, in set9]
IntegerProps.fct_to_list_unique [lemma, in set9]
IntegerProps.fct_to_rev [lemma, in set9]
IntegerProps.finite_c_set [lemma, in set9]
IntegerProps.finite_int_fam [definition, in set9]
IntegerProps.finite_lt_a_ab [lemma, in set9]
IntegerProps.finite_ordered_interval [lemma, in set9]
IntegerProps.finite_ordered_interval1 [lemma, in set9]
IntegerProps.finite_powerset [lemma, in set9]
IntegerProps.finite_power_lt1 [lemma, in set9]
IntegerProps.finite_power_lt1N [lemma, in set9]
IntegerProps.finite_power_lt2 [lemma, in set9]
IntegerProps.finite_power_lt2N [lemma, in set9]
IntegerProps.finite_product_finite [lemma, in set9]
IntegerProps.finite_product_finite_aux [lemma, in set9]
IntegerProps.finite_product_finite_set [lemma, in set9]
IntegerProps.finite_product_lt [lemma, in set9]
IntegerProps.finite_prod2_lt [lemma, in set9]
IntegerProps.finite_set_interval_Bnat [lemma, in set9]
IntegerProps.finite_set_interval_co [lemma, in set9]
IntegerProps.finite_sum2_lt [lemma, in set9]
IntegerProps.finite_sum3_lt [lemma, in set9]
IntegerProps.finite_sum_finite [lemma, in set9]
IntegerProps.finite_sum_finite_aux [lemma, in set9]
IntegerProps.finite_sum_lt [lemma, in set9]
IntegerProps.finite_union_finite [lemma, in set9]
IntegerProps.function_on_nat [definition, in set9]
IntegerProps.function_on_nat_pr [lemma, in set9]
IntegerProps.function_on_nat_pr1 [lemma, in set9]
IntegerProps.iid_function [definition, in set9]
IntegerProps.increasing_compose [lemma, in set9]
IntegerProps.increasing_compose3 [lemma, in set9]
IntegerProps.increasing_prop [lemma, in set9]
IntegerProps.increasing_prop1 [lemma, in set9]
IntegerProps.inc_a_interval_co_succ [lemma, in set9]
IntegerProps.inc_function_on_nat_Bnat [lemma, in set9]
IntegerProps.inc_quotient_bnat [lemma, in set9]
IntegerProps.inc_remainder_bnat [lemma, in set9]
IntegerProps.induction_on_prod [lemma, in set9]
IntegerProps.induction_on_prod0 [lemma, in set9]
IntegerProps.induction_on_prod1 [lemma, in set9]
IntegerProps.induction_on_prod2 [lemma, in set9]
IntegerProps.induction_on_prod4 [lemma, in set9]
IntegerProps.induction_on_prod5 [lemma, in set9]
IntegerProps.induction_on_sum [lemma, in set9]
IntegerProps.induction_on_sum0 [lemma, in set9]
IntegerProps.induction_on_sum1 [lemma, in set9]
IntegerProps.induction_on_sum2 [lemma, in set9]
IntegerProps.induction_on_sum3 [lemma, in set9]
IntegerProps.induction_on_sum4 [lemma, in set9]
IntegerProps.induction_on_sum5 [lemma, in set9]
IntegerProps.interval_Bnat [definition, in set9]
IntegerProps.interval_Bnatco [definition, in set9]
IntegerProps.interval_Bnatco_related [lemma, in set9]
IntegerProps.interval_Bnatco_substrate [lemma, in set9]
IntegerProps.interval_Bnatco_worder [lemma, in set9]
IntegerProps.interval_Bnato [definition, in set9]
IntegerProps.interval_Bnato_related [lemma, in set9]
IntegerProps.interval_Bnato_related1 [lemma, in set9]
IntegerProps.interval_Bnato_related2 [lemma, in set9]
IntegerProps.interval_Bnato_substrate [lemma, in set9]
IntegerProps.interval_Bnato_worder [lemma, in set9]
IntegerProps.interval_Bnat_pr [lemma, in set9]
IntegerProps.interval_Bnat_pr0 [lemma, in set9]
IntegerProps.interval_cc_0a_increasing [lemma, in set9]
IntegerProps.interval_cc_0a_increasing1 [lemma, in set9]
IntegerProps.interval_co_cc [lemma, in set9]
IntegerProps.interval_co_pr4 [lemma, in set9]
IntegerProps.interval_co_0a [definition, in set9]
IntegerProps.interval_co_0a_increasing [lemma, in set9]
IntegerProps.interval_co_0a_increasing1 [lemma, in set9]
IntegerProps.interval_co_0a_pr [lemma, in set9]
IntegerProps.interval_co_0a_pr1 [lemma, in set9]
IntegerProps.interval_co_0a_pr2 [lemma, in set9]
IntegerProps.interval_co_0a_pr3 [lemma, in set9]
IntegerProps.interval_co_0a_restr [lemma, in set9]
IntegerProps.isomorphism_worder_finite [lemma, in set9]
IntegerProps.is_expansion [definition, in set9]
IntegerProps.is_expansion_exists [lemma, in set9]
IntegerProps.is_expansion_exists1 [lemma, in set9]
IntegerProps.is_expansion_prop0 [lemma, in set9]
IntegerProps.is_expansion_prop1 [lemma, in set9]
IntegerProps.is_expansion_prop10 [lemma, in set9]
IntegerProps.is_expansion_prop11 [lemma, in set9]
IntegerProps.is_expansion_prop2 [lemma, in set9]
IntegerProps.is_expansion_prop3 [lemma, in set9]
IntegerProps.is_expansion_prop4 [lemma, in set9]
IntegerProps.is_expansion_prop5 [lemma, in set9]
IntegerProps.is_expansion_prop6 [lemma, in set9]
IntegerProps.is_expansion_prop7 [lemma, in set9]
IntegerProps.is_expansion_prop8 [lemma, in set9]
IntegerProps.is_expansion_prop9 [lemma, in set9]
IntegerProps.is_expansion_unique [lemma, in set9]
IntegerProps.is_finite_in_product [lemma, in set9]
IntegerProps.least_int_prop [lemma, in set9]
IntegerProps.least_int_prop0 [lemma, in set9]
IntegerProps.least_int_prop1 [lemma, in set9]
IntegerProps.length_app1 [lemma, in set9]
IntegerProps.length_app2 [lemma, in set9]
IntegerProps.le_one_not_zero [lemma, in set9]
IntegerProps.list_extens [lemma, in set9]
IntegerProps.list_prod [definition, in set9]
IntegerProps.list_prod_app [lemma, in set9]
IntegerProps.list_prod_cons [lemma, in set9]
IntegerProps.list_prod_consr [lemma, in set9]
IntegerProps.list_prod_pr [lemma, in set9]
IntegerProps.list_prod_rev [lemma, in set9]
IntegerProps.list_prod_single [lemma, in set9]
IntegerProps.list_prop [inductive, in set9]
IntegerProps.list_prop1 [lemma, in set9]
IntegerProps.list_prop2 [lemma, in set9]
IntegerProps.list_prop3 [lemma, in set9]
IntegerProps.list_prop_app [lemma, in set9]
IntegerProps.list_prop_cons [constructor, in set9]
IntegerProps.list_prop_nil [constructor, in set9]
IntegerProps.list_prop_nth [lemma, in set9]
IntegerProps.list_prop_refine [lemma, in set9]
IntegerProps.list_range [definition, in set9]
IntegerProps.list_range_pr [lemma, in set9]
IntegerProps.list_range_pr1 [lemma, in set9]
IntegerProps.list_subset [definition, in set9]
IntegerProps.list_subset_cons [lemma, in set9]
IntegerProps.list_sum [definition, in set9]
IntegerProps.list_sum_app [lemma, in set9]
IntegerProps.list_sum_cons [lemma, in set9]
IntegerProps.list_sum_consr [lemma, in set9]
IntegerProps.list_sum_pr [lemma, in set9]
IntegerProps.list_sum_rev [lemma, in set9]
IntegerProps.list_sum_single [lemma, in set9]
IntegerProps.list_to_f [definition, in set9]
IntegerProps.list_to_fB [definition, in set9]
IntegerProps.list_to_fB_axioms [lemma, in set9]
IntegerProps.list_to_fB_function [lemma, in set9]
IntegerProps.list_to_fB_pr [lemma, in set9]
IntegerProps.list_to_fB_W [lemma, in set9]
IntegerProps.list_to_fB_W1 [lemma, in set9]
IntegerProps.list_to_fct [definition, in set9]
IntegerProps.list_to_fctB [definition, in set9]
IntegerProps.list_to_fct_pr [lemma, in set9]
IntegerProps.list_to_fct_pr0 [lemma, in set9]
IntegerProps.list_to_fct_pr0B [lemma, in set9]
IntegerProps.list_to_fct_pr1 [lemma, in set9]
IntegerProps.list_to_fct_pr1B [lemma, in set9]
IntegerProps.list_to_fct_pr3 [lemma, in set9]
IntegerProps.list_to_fct_pr3B [lemma, in set9]
IntegerProps.list_to_fct_pr4 [lemma, in set9]
IntegerProps.list_to_fct_pr4B [lemma, in set9]
IntegerProps.list_to_f_axioms [lemma, in set9]
IntegerProps.list_to_f_consB0 [lemma, in set9]
IntegerProps.list_to_f_consB1 [lemma, in set9]
IntegerProps.list_to_f_consB2 [lemma, in set9]
IntegerProps.list_to_f_consB3 [lemma, in set9]
IntegerProps.list_to_f_cons0 [lemma, in set9]
IntegerProps.list_to_f_cons1 [lemma, in set9]
IntegerProps.list_to_f_cons2 [lemma, in set9]
IntegerProps.list_to_f_cons3 [lemma, in set9]
IntegerProps.list_to_f_function [lemma, in set9]
IntegerProps.list_to_f_pr1 [lemma, in set9]
IntegerProps.list_to_f_pr2 [lemma, in set9]
IntegerProps.list_to_f_W [lemma, in set9]
IntegerProps.list_to_f_W1 [lemma, in set9]
IntegerProps.list_to_f_W2 [lemma, in set9]
IntegerProps.lt_a_power_b_a [lemma, in set9]
IntegerProps.lt_a_power_b_aN [lemma, in set9]
IntegerProps.lt_i_n [lemma, in set9]
IntegerProps.lt_n_succ_le [lemma, in set9]
IntegerProps.lt_n_succ_leN [lemma, in set9]
IntegerProps.lt_plus [lemma, in set9]
IntegerProps.lt_to_plus [lemma, in set9]
IntegerProps.l_to_fct [lemma, in set9]
IntegerProps.l_to_fct1 [lemma, in set9]
IntegerProps.l_to_fct2 [lemma, in set9]
IntegerProps.minus_n_nC [lemma, in set9]
IntegerProps.minus_n_0C [lemma, in set9]
IntegerProps.minus_SnSi [lemma, in set9]
IntegerProps.minus_wrong [lemma, in set9]
IntegerProps.mult_le_lt_compat [lemma, in set9]
IntegerProps.mult_lt_le_compat [lemma, in set9]
IntegerProps.mult_lt_reg_l [lemma, in set9]
IntegerProps.mult_lt_reg_r [lemma, in set9]
IntegerProps.mult_simplifiable_left [lemma, in set9]
IntegerProps.mult_simplifiable_leftN [lemma, in set9]
IntegerProps.mult_simplifiable_right [lemma, in set9]
IntegerProps.mult_simplifiable_rightN [lemma, in set9]
IntegerProps.mult_S_lt_reg_l [lemma, in set9]
IntegerProps.mutually_disjoint_prop1 [lemma, in set9]
IntegerProps.nat_B_division [lemma, in set9]
IntegerProps.nat_B_pow [lemma, in set9]
IntegerProps.nat_B_pred [lemma, in set9]
IntegerProps.nat_B_quo [lemma, in set9]
IntegerProps.nat_B_rem [lemma, in set9]
IntegerProps.nat_B_sub [lemma, in set9]
IntegerProps.nat_not_zero_pr [lemma, in set9]
IntegerProps.Ndivides [definition, in set9]
IntegerProps.Ndivides_itself [lemma, in set9]
IntegerProps.Ndivides_pr [lemma, in set9]
IntegerProps.Ndivides_pr1 [lemma, in set9]
IntegerProps.Ndivides_pr2 [lemma, in set9]
IntegerProps.Ndivides_pr3 [lemma, in set9]
IntegerProps.Ndivides_pr4 [lemma, in set9]
IntegerProps.Ndivides_trans [lemma, in set9]
IntegerProps.Ndivides_trans1 [lemma, in set9]
IntegerProps.Ndivides_trans2 [lemma, in set9]
IntegerProps.Ndivision_existence [lemma, in set9]
IntegerProps.Ndivision_exists [lemma, in set9]
IntegerProps.Ndivision_itself [lemma, in set9]
IntegerProps.Ndivision_of_zero [lemma, in set9]
IntegerProps.Ndivision_pr [lemma, in set9]
IntegerProps.Ndivision_pr_q [lemma, in set9]
IntegerProps.Ndivision_pr_r [lemma, in set9]
IntegerProps.Ndivision_unique [lemma, in set9]
IntegerProps.nonzero_suc [lemma, in set9]
IntegerProps.non_zero_apowb [lemma, in set9]
IntegerProps.non_zero_apowbN [lemma, in set9]
IntegerProps.non_zero_mult [lemma, in set9]
IntegerProps.Nquo [definition, in set9]
IntegerProps.Nquo_itself [lemma, in set9]
IntegerProps.Nquo_simplify [lemma, in set9]
IntegerProps.Nrem [definition, in set9]
IntegerProps.number_of_injections [definition, in set9]
IntegerProps.number_of_injections_base [lemma, in set9]
IntegerProps.number_of_injections_pr [lemma, in set9]
IntegerProps.number_of_injections_prop [lemma, in set9]
IntegerProps.number_of_injections_rec [lemma, in set9]
IntegerProps.number_of_partitions [lemma, in set9]
IntegerProps.number_of_partitions1 [lemma, in set9]
IntegerProps.number_of_partitions2 [lemma, in set9]
IntegerProps.number_of_partitions3 [lemma, in set9]
IntegerProps.number_of_partitions4 [lemma, in set9]
IntegerProps.number_of_partitions5 [lemma, in set9]
IntegerProps.number_of_partitions6 [lemma, in set9]
IntegerProps.number_of_partitions7 [lemma, in set9]
IntegerProps.number_of_partitions_bis [lemma, in set9]
IntegerProps.number_of_permutations [lemma, in set9]
IntegerProps.O [definition, in set9]
IntegerProps.one_divides_all [lemma, in set9]
IntegerProps.partition_complement [lemma, in set9]
IntegerProps.partition_tack_on [lemma, in set9]
IntegerProps.partition_tack_on_intco [lemma, in set9]
IntegerProps.partition_with_pi_elements [definition, in set9]
IntegerProps.plus_minusC [lemma, in set9]
IntegerProps.plus_n_Sm_subSm [lemma, in set9]
IntegerProps.plus_n_Sm_subSn [lemma, in set9]
IntegerProps.plus_reg_r [lemma, in set9]
IntegerProps.plus_simplifiable_left [lemma, in set9]
IntegerProps.plus_simplifiable_leftN [lemma, in set9]
IntegerProps.plus_simplifiable_right [lemma, in set9]
IntegerProps.plus_simplifiable_rightN [lemma, in set9]
IntegerProps.power_of_prodN [lemma, in set9]
IntegerProps.power_of_sumN [lemma, in set9]
IntegerProps.power_x_0N [lemma, in set9]
IntegerProps.power_x_1N [lemma, in set9]
IntegerProps.power_0_x [lemma, in set9]
IntegerProps.power_0_0N [lemma, in set9]
IntegerProps.power_1_xN [lemma, in set9]
IntegerProps.power_2_4 [lemma, in set9]
IntegerProps.pow_succ [lemma, in set9]
IntegerProps.prec_pr1 [lemma, in set9]
IntegerProps.pred_minus [lemma, in set9]
IntegerProps.prod_increasing6 [lemma, in set9]
IntegerProps.quotient_by_one [lemma, in set9]
IntegerProps.quotient_of_factorials [lemma, in set9]
IntegerProps.quotient_of_factorials1 [lemma, in set9]
IntegerProps.restr_plus_interval_isomorphism [lemma, in set9]
IntegerProps.restr_plus_minus_bij [lemma, in set9]
IntegerProps.rest_minus_interval [definition, in set9]
IntegerProps.rest_minus_interval_axioms [lemma, in set9]
IntegerProps.rest_plus_interval [definition, in set9]
IntegerProps.rest_plus_interval_axioms [lemma, in set9]
IntegerProps.set_of_functions_sum0 [lemma, in set9]
IntegerProps.set_of_functions_sum1 [lemma, in set9]
IntegerProps.set_of_functions_sum2 [lemma, in set9]
IntegerProps.set_of_functions_sum3 [lemma, in set9]
IntegerProps.set_of_functions_sum4 [lemma, in set9]
IntegerProps.set_of_functions_sum_eq [definition, in set9]
IntegerProps.set_of_functions_sum_le [definition, in set9]
IntegerProps.set_of_functions_sum_le_int [definition, in set9]
IntegerProps.set_of_functions_sum_pr [lemma, in set9]
IntegerProps.set_of_increasing_functions_int [definition, in set9]
IntegerProps.set_of_injections [definition, in set9]
IntegerProps.set_of_partitions [definition, in set9]
IntegerProps.set_of_partitions_aux [definition, in set9]
IntegerProps.shepherd_principle [lemma, in set9]
IntegerProps.Sn_is_plus1 [lemma, in set9]
IntegerProps.Sn_is_1plus [lemma, in set9]
IntegerProps.special_cardinal_positive [lemma, in set9]
IntegerProps.strict_increasing_prop [lemma, in set9]
IntegerProps.strict_increasing_prop1 [lemma, in set9]
IntegerProps.strict_increasing_prop2 [lemma, in set9]
IntegerProps.strict_increasing_prop3 [lemma, in set9]
IntegerProps.subsets_with_p_elements [definition, in set9]
IntegerProps.subsets_with_p_elements_pr [lemma, in set9]
IntegerProps.sub_increasing2 [lemma, in set9]
IntegerProps.sub_interval_Bnat [lemma, in set9]
IntegerProps.sub_interval_co_0a_Bnat [lemma, in set9]
IntegerProps.sub_le_symmetry [lemma, in set9]
IntegerProps.sub_lt_symmetry [lemma, in set9]
IntegerProps.sum_increasing4 [lemma, in set9]
IntegerProps.sum_increasing5 [lemma, in set9]
IntegerProps.sum_increasing6 [lemma, in set9]
IntegerProps.sum_of_binomial [lemma, in set9]
IntegerProps.sum_of_binomial1 [lemma, in set9]
IntegerProps.sum_of_binomial2 [lemma, in set9]
IntegerProps.sum_of_i [lemma, in set9]
IntegerProps.sum_of_i2 [lemma, in set9]
IntegerProps.sum_of_i3 [lemma, in set9]
IntegerProps.sum_to_increasing1 [lemma, in set9]
IntegerProps.sum_to_increasing2 [lemma, in set9]
IntegerProps.sum_to_increasing4 [lemma, in set9]
IntegerProps.sum_to_increasing5 [lemma, in set9]
IntegerProps.sum_to_increasing6 [lemma, in set9]
IntegerProps.sum_to_increasing_fct [definition, in set9]
IntegerProps.sum_to_increasing_fun [definition, in set9]
IntegerProps.tack_on_nat [lemma, in set9]
IntegerProps.trivial_cardinal_prod3 [lemma, in set9]
IntegerProps.trivial_cardinal_sum3 [lemma, in set9]
IntegerProps.two_plus_two [lemma, in set9]
IntegerProps.two_times_n [lemma, in set9]
IntegerProps.two_times_two [lemma, in set9]
IntegerProps.zero_lt_oneN [lemma, in set9]
Intersection [module, in set1]
Intersection.intersection [definition, in set1]
Intersection.intersection2 [definition, in set1]
Intersection.intersection2comm [lemma, in set1]
Intersection.intersection2idem [lemma, in set1]
Intersection.intersection2sub_first [lemma, in set1]
Intersection.intersection2sub_second [lemma, in set1]
Intersection.intersection2_both [lemma, in set1]
Intersection.intersection2_first [lemma, in set1]
Intersection.intersection2_inc [lemma, in set1]
Intersection.intersection2_second [lemma, in set1]
Intersection.intersection2_sub [lemma, in set1]
Intersection.intersection_forall [lemma, in set1]
Intersection.intersection_inc [lemma, in set1]
Intersection.intersection_sub [lemma, in set1]
L
Little [module, in set1]Little.doubleton [definition, in set1]
Little.doubleton_first [lemma, in set1]
Little.doubleton_inj [lemma, in set1]
Little.doubleton_or [lemma, in set1]
Little.doubleton_rw [lemma, in set1]
Little.doubleton_second [lemma, in set1]
Little.doubleton_singleton [lemma, in set1]
Little.doubleton_symm [lemma, in set1]
Little.inc_TPa_two_points [lemma, in set1]
Little.inc_TPb_two_points [lemma, in set1]
Little.nonempty_doubleton [lemma, in set1]
Little.nonempty_singleton [lemma, in set1]
Little.one_point [inductive, in set1]
Little.one_point_intro [constructor, in set1]
Little.singleton [definition, in set1]
Little.singleton_eq [lemma, in set1]
Little.singleton_inc [lemma, in set1]
Little.singleton_inj [lemma, in set1]
Little.singleton_rw [lemma, in set1]
Little.sub_doubleton [lemma, in set1]
Little.sub_singleton [lemma, in set1]
Little.TPa [definition, in set1]
Little.TPb [definition, in set1]
Little.two_points [inductive, in set1]
Little.two_points_a [constructor, in set1]
Little.two_points_b [constructor, in set1]
Little.two_points_distinct [lemma, in set1]
Little.two_points_distinctb [lemma, in set1]
Little.two_points_pr [lemma, in set1]
Little.two_points_pr2 [lemma, in set1]
O
Ordinals [module, in set11]Ordinals.canonical2_substrate [lemma, in set11]
Ordinals.canonical_du2 [definition, in set11]
Ordinals.canonical_du2_pr [lemma, in set11]
Ordinals.canonical_du2_rw [lemma, in set11]
Ordinals.du_index_pr [lemma, in set11]
Ordinals.du_index_pr1 [lemma, in set11]
Ordinals.emptyset_order [lemma, in set11]
Ordinals.emptyset_substrate [lemma, in set11]
Ordinals.inc_disjoint_union [lemma, in set11]
Ordinals.inc_disjoint_union1 [lemma, in set11]
Ordinals.is_order_type [definition, in set11]
Ordinals.is_ordinal [definition, in set11]
Ordinals.is_ordinal_omega [lemma, in set11]
Ordinals.is_ordinal_0 [lemma, in set11]
Ordinals.is_ordinal_1 [lemma, in set11]
Ordinals.is_ordinal_2 [lemma, in set11]
Ordinals.lexorder_gle1 [lemma, in set11]
Ordinals.lexorder_worder [lemma, in set11]
Ordinals.order_isomorphic [definition, in set11]
Ordinals.order_isomorphic_reflexive [lemma, in set11]
Ordinals.order_isomorphic_symmetric [lemma, in set11]
Ordinals.order_isomorphic_transitive [lemma, in set11]
Ordinals.order_isomorphism_pr [lemma, in set11]
Ordinals.order_isomorphism_pr1 [lemma, in set11]
Ordinals.order_isomorphism_pr2 [lemma, in set11]
Ordinals.order_prod_invariant4 [lemma, in set11]
Ordinals.order_sum_invariant4 [lemma, in set11]
Ordinals.order_type [definition, in set11]
Ordinals.order_type_le [definition, in set11]
Ordinals.order_type_le_preorder [lemma, in set11]
Ordinals.ordinal0_pr [lemma, in set11]
Ordinals.ordinal0_pr1 [lemma, in set11]
Ordinals.ordinal_product2 [definition, in set11]
Ordinals.ordinal_product2_gle [lemma, in set11]
Ordinals.ordinal_product2_order [lemma, in set11]
Ordinals.ordinal_product2_substrate [lemma, in set11]
Ordinals.ordinal_product2_worder [lemma, in set11]
Ordinals.ordinal_product_pr [lemma, in set11]
Ordinals.ordinal_product_pr1 [lemma, in set11]
Ordinals.ordinal_product_pr2 [lemma, in set11]
Ordinals.ordinal_product_pr3 [lemma, in set11]
Ordinals.ordinal_product_pr4 [lemma, in set11]
Ordinals.ordinal_prod2_axioms [lemma, in set11]
Ordinals.ordinal_pr1 [lemma, in set11]
Ordinals.ordinal_pr10 [lemma, in set11]
Ordinals.ordinal_pr2 [lemma, in set11]
Ordinals.ordinal_pr3 [lemma, in set11]
Ordinals.ordinal_pr4 [lemma, in set11]
Ordinals.ordinal_pr5 [lemma, in set11]
Ordinals.ordinal_pr6 [lemma, in set11]
Ordinals.ordinal_pr7 [lemma, in set11]
Ordinals.ordinal_pr8 [lemma, in set11]
Ordinals.ordinal_pr9 [lemma, in set11]
Ordinals.ordinal_sum [definition, in set11]
Ordinals.ordinal_sum2 [definition, in set11]
Ordinals.ordinal_sum2_axioms [lemma, in set11]
Ordinals.ordinal_sum2_gle [lemma, in set11]
Ordinals.ordinal_sum2_gle_spec [lemma, in set11]
Ordinals.ordinal_sum2_order [lemma, in set11]
Ordinals.ordinal_sum2_substrate [lemma, in set11]
Ordinals.ordinal_sum2_totalorder [lemma, in set11]
Ordinals.ordinal_sum2_worder [lemma, in set11]
Ordinals.ordinal_sum_assoc [definition, in set11]
Ordinals.ordinal_sum_assoc1 [lemma, in set11]
Ordinals.ordinal_sum_assoc_aux [definition, in set11]
Ordinals.ordinal_sum_assoc_aux1 [lemma, in set11]
Ordinals.ordinal_sum_assoc_aux2 [lemma, in set11]
Ordinals.ordinal_sum_assoc_aux3 [lemma, in set11]
Ordinals.ordinal_sum_assoc_iso [lemma, in set11]
Ordinals.ordinal_sum_axioms [definition, in set11]
Ordinals.ordinal_sum_axioms1 [definition, in set11]
Ordinals.ordinal_sum_distributive [lemma, in set11]
Ordinals.ordinal_sum_order [lemma, in set11]
Ordinals.ordinal_sum_r [definition, in set11]
Ordinals.ordinal_sum_related [lemma, in set11]
Ordinals.ordinal_sum_related1 [lemma, in set11]
Ordinals.ordinal_sum_related_id [lemma, in set11]
Ordinals.ordinal_sum_substrate [lemma, in set11]
Ordinals.ordinal_sum_totalorder [lemma, in set11]
Ordinals.ordinal_sum_worder [lemma, in set11]
Ordinals.ordinal_1_indep [lemma, in set11]
Ordinals.ordinal_1_value [lemma, in set11]
Ordinals.ordinal_1_value_bis [lemma, in set11]
Ordinals.ord_omega [definition, in set11]
Ordinals.ord_one [definition, in set11]
Ordinals.ord_prod [definition, in set11]
Ordinals.ord_prod2 [definition, in set11]
Ordinals.ord_prod2_ordinal [lemma, in set11]
Ordinals.ord_prod2_pr [lemma, in set11]
Ordinals.ord_prod2_type [lemma, in set11]
Ordinals.ord_prod_emptyset [lemma, in set11]
Ordinals.ord_prod_invariant1 [lemma, in set11]
Ordinals.ord_prod_invariant2 [lemma, in set11]
Ordinals.ord_prod_invariant3 [lemma, in set11]
Ordinals.ord_prod_ordinal [lemma, in set11]
Ordinals.ord_prod_singleton [lemma, in set11]
Ordinals.ord_prod_type [lemma, in set11]
Ordinals.ord_sum [definition, in set11]
Ordinals.ord_sum2 [definition, in set11]
Ordinals.ord_sum2_ordinal [lemma, in set11]
Ordinals.ord_sum2_pr [lemma, in set11]
Ordinals.ord_sum2_type [lemma, in set11]
Ordinals.ord_sum_emptyset [lemma, in set11]
Ordinals.ord_sum_invariant1 [lemma, in set11]
Ordinals.ord_sum_invariant2 [lemma, in set11]
Ordinals.ord_sum_invariant3 [lemma, in set11]
Ordinals.ord_sum_ordinal [lemma, in set11]
Ordinals.ord_sum_singleton [lemma, in set11]
Ordinals.ord_sum_type [lemma, in set11]
Ordinals.ord_two [definition, in set11]
Ordinals.ord_zero [definition, in set11]
Ordinals.ord_0_plus_unit_l [lemma, in set11]
Ordinals.ord_0_plus_unit_r [lemma, in set11]
Ordinals.ord_0_prod_l [lemma, in set11]
Ordinals.ord_0_prod_r [lemma, in set11]
Ordinals.ord_1_mult_unit_l [lemma, in set11]
Ordinals.ord_1_mult_unit_r [lemma, in set11]
Ordinals.prod_of_substrates_pr [lemma, in set11]
Ordinals.singleton_order_isomorphic [lemma, in set11]
Ordinals.singleton_order_isomorphic1 [lemma, in set11]
Ordinals.singleton_order_isomorphic2 [lemma, in set11]
Ordinals.singleton_worder [lemma, in set11]
Ordinals.sum_of_substrates [definition, in set11]
Ordinals.worder_invariance [lemma, in set11]
P
Pair [module, in set1]Pair.bpair_x [definition, in set1]
Pair.is_kpair [definition, in set1]
Pair.is_pair [definition, in set1]
Pair.is_pair_rw [lemma, in set1]
Pair.kpair [definition, in set1]
Pair.kpair_recov [lemma, in set1]
Pair.kpr0_pair [lemma, in set1]
Pair.kpr1 [definition, in set1]
Pair.kpr1_def [lemma, in set1]
Pair.kpr1_pair [lemma, in set1]
Pair.kpr2 [definition, in set1]
Pair.kpr2_def [lemma, in set1]
Pair.kpr2_pair [lemma, in set1]
Pair.P [definition, in set1]
Pair.pair_distinct [lemma, in set1]
Pair.pair_distincta [lemma, in set1]
Pair.pair_extensionality [lemma, in set1]
Pair.pair_first [definition, in set1]
Pair.pair_is_kpair [lemma, in set1]
Pair.pair_is_pair [lemma, in set1]
Pair.pair_recov [lemma, in set1]
Pair.pair_second [definition, in set1]
Pair.pr1_def [lemma, in set1]
Pair.pr1_injective_x [lemma, in set1]
Pair.pr1_pair [lemma, in set1]
Pair.pr2_def [lemma, in set1]
Pair.pr2_injective_x [lemma, in set1]
Pair.pr2_pair [lemma, in set1]
Pair.Q [definition, in set1]
Pair.V [definition, in set1]
Pair.V_inc [lemma, in set1]
Pair.V_or [lemma, in set1]
pair_constructor [axiom, in set1]
Powerset [module, in set1]
Powerset.inc_x_powerset_x [lemma, in set1]
Powerset.powerset [definition, in set1]
Powerset.powerset_inc [lemma, in set1]
Powerset.powerset_inc_rw [lemma, in set1]
Powerset.powerset_sub [lemma, in set1]
prod_extensionality [axiom, in set1]
R
Relation [module, in set4]Relation.all_equivalence_relations [definition, in set4]
Relation.all_relations [definition, in set4]
Relation.canonical_decomposition [lemma, in set4]
Relation.canonical_decompositiona [lemma, in set4]
Relation.canonical_decompositionb [lemma, in set4]
Relation.canonical_decomposition_surj [lemma, in set4]
Relation.canonical_decomposition_surj2 [lemma, in set4]
Relation.canonical_foq_induced_rel [definition, in set4]
Relation.canonical_foq_induced_rel_bijective [lemma, in set4]
Relation.canon_proj [definition, in set4]
Relation.canon_proj_diagonal_bijective [lemma, in set4]
Relation.canon_proj_function [lemma, in set4]
Relation.canon_proj_inc [lemma, in set4]
Relation.canon_proj_show_surjective [lemma, in set4]
Relation.canon_proj_source [lemma, in set4]
Relation.canon_proj_surjective [lemma, in set4]
Relation.canon_proj_target [lemma, in set4]
Relation.canon_proj_W [lemma, in set4]
Relation.class [definition, in set4]
Relation.class_dichot [lemma, in set4]
Relation.class_is_cut [lemma, in set4]
Relation.class_is_inv_direct_value [lemma, in set4]
Relation.class_prod_of_rel2 [lemma, in set4]
Relation.class_rep [lemma, in set4]
Relation.coarse [definition, in set4]
Relation.coarsest_equivalence [lemma, in set4]
Relation.coarse_equivalence [lemma, in set4]
Relation.coarse_graph [lemma, in set4]
Relation.coarse_related [lemma, in set4]
Relation.coarse_substrate [lemma, in set4]
Relation.compatible_constant_on_classes [lemma, in set4]
Relation.compatible_constant_on_classes2 [lemma, in set4]
Relation.compatible_ea [lemma, in set4]
Relation.compatible_ext_to_prod [lemma, in set4]
Relation.compatible_ext_to_prod_inv [lemma, in set4]
Relation.compatible_injection_induced_rel [lemma, in set4]
Relation.compatible_with_equiv [definition, in set4]
Relation.compatible_with_equivs [definition, in set4]
Relation.compatible_with_equiv_p [definition, in set4]
Relation.compatible_with_equiv_pr [lemma, in set4]
Relation.compatible_with_finer [lemma, in set4]
Relation.compatible_with_pr [lemma, in set4]
Relation.compatible_with_proj [lemma, in set4]
Relation.compatible_with_proj3 [lemma, in set4]
Relation.compatible_with_pr2 [lemma, in set4]
Relation.composable_fun_proj [lemma, in set4]
Relation.composable_fun_projc [lemma, in set4]
Relation.composable_fun_projcs [lemma, in set4]
Relation.composable_fun_projs [lemma, in set4]
Relation.compose_foq_proj [lemma, in set4]
Relation.compose_fun_proj_eq [lemma, in set4]
Relation.compose_fun_proj_eq2 [lemma, in set4]
Relation.compose_fun_proj_ev [lemma, in set4]
Relation.compose_fun_proj_ev2 [lemma, in set4]
Relation.cqr_aux [lemma, in set4]
Relation.decomposable_ext_to_prod_rel [lemma, in set4]
Relation.diagonal_class [lemma, in set4]
Relation.diagonal_equivalence [lemma, in set4]
Relation.diagonal_equivalence1 [lemma, in set4]
Relation.diagonal_equivalence2 [lemma, in set4]
Relation.diagonal_substrate [lemma, in set4]
Relation.domain_is_substrate [lemma, in set4]
Relation.ea_equivalence [lemma, in set4]
Relation.ea_foq_injective [lemma, in set4]
Relation.ea_foq_on_im_bijective [lemma, in set4]
Relation.ea_related [lemma, in set4]
Relation.equipotent_equivalence [lemma, in set4]
Relation.equivalence_associated [definition, in set4]
Relation.equivalence_equivalence [lemma, in set4]
Relation.equivalence_has_graph [lemma, in set4]
Relation.equivalence_has_graph0 [lemma, in set4]
Relation.equivalence_has_graph2 [lemma, in set4]
Relation.equivalence_if_has_graph [lemma, in set4]
Relation.equivalence_if_has_graph2 [lemma, in set4]
Relation.equivalence_is_graph [lemma, in set4]
Relation.equivalence_pr [lemma, in set4]
Relation.equivalence_prod_of_rel [lemma, in set4]
Relation.equivalence_r [definition, in set4]
Relation.equivalence_re [definition, in set4]
Relation.equivalence_relation_bourbaki_ex5 [lemma, in set4]
Relation.equivalence_relation_pr1 [lemma, in set4]
Relation.eq_rel_associated [definition, in set4]
Relation.exists_fun_on_quotient [lemma, in set4]
Relation.exists_unique_fun_on_quotient [lemma, in set4]
Relation.ext_to_prod_rel_function [lemma, in set4]
Relation.ext_to_prod_rel_W [lemma, in set4]
Relation.finer_axioms [definition, in set4]
Relation.finer_equivalence [definition, in set4]
Relation.finer_sub_equiv [lemma, in set4]
Relation.finer_sub_equiv2 [lemma, in set4]
Relation.finer_sub_equiv3 [lemma, in set4]
Relation.finest_equivalence [lemma, in set4]
Relation.first_proj_class [lemma, in set4]
Relation.first_proj_eq [definition, in set4]
Relation.first_proj_eqr [definition, in set4]
Relation.first_proj_equivalence [lemma, in set4]
Relation.first_proj_equiv_proj [lemma, in set4]
Relation.first_proj_eq_pr [lemma, in set4]
Relation.first_proj_eq_related [lemma, in set4]
Relation.first_proj_graph [lemma, in set4]
Relation.first_proj_substrate [lemma, in set4]
Relation.foqcs_axioms [lemma, in set4]
Relation.foqcs_function [lemma, in set4]
Relation.foqcs_W [lemma, in set4]
Relation.foqc_axioms [lemma, in set4]
Relation.foqc_function [lemma, in set4]
Relation.foqc_W [lemma, in set4]
Relation.foqs_axioms [lemma, in set4]
Relation.foqs_function [lemma, in set4]
Relation.foqs_W [lemma, in set4]
Relation.foq_axioms [lemma, in set4]
Relation.foq_finer_function [lemma, in set4]
Relation.foq_finer_surjective [lemma, in set4]
Relation.foq_finer_W [lemma, in set4]
Relation.foq_function [lemma, in set4]
Relation.foq_induced_rel_image [lemma, in set4]
Relation.foq_induced_rel_injective [lemma, in set4]
Relation.foq_W [lemma, in set4]
Relation.function_on_quotient [definition, in set4]
Relation.function_on_quotients [definition, in set4]
Relation.fun_on_quotient [definition, in set4]
Relation.fun_on_quotients [definition, in set4]
Relation.fun_on_quotient_pr [lemma, in set4]
Relation.fun_on_quotient_pr2 [lemma, in set4]
Relation.fun_on_quotient_pr3 [lemma, in set4]
Relation.fun_on_quotient_pr4 [lemma, in set4]
Relation.fun_on_quotient_pr5 [lemma, in set4]
Relation.fun_on_rep [definition, in set4]
Relation.fun_on_reps [definition, in set4]
Relation.graph_ea_equivalence [lemma, in set4]
Relation.graph_ea_substrate [lemma, in set4]
Relation.graph_of_ea [lemma, in set4]
Relation.graph_on [definition, in set4]
Relation.graph_on_graph [lemma, in set4]
Relation.graph_on_rw0 [lemma, in set4]
Relation.graph_on_rw1 [lemma, in set4]
Relation.graph_on_rw2 [lemma, in set4]
Relation.graph_on_substrate [lemma, in set4]
Relation.idempotent_graph_transitive [lemma, in set4]
Relation.iirel_axioms [definition, in set4]
Relation.iirel_class [lemma, in set4]
Relation.iirel_function [lemma, in set4]
Relation.iirel_related [lemma, in set4]
Relation.iirel_relation [lemma, in set4]
Relation.iirel_substrate [lemma, in set4]
Relation.inc_all_equivalence_relations [lemma, in set4]
Relation.inc_all_relations [lemma, in set4]
Relation.inc_arg1_substrate [lemma, in set4]
Relation.inc_arg2_substrate [lemma, in set4]
Relation.inc_class [lemma, in set4]
Relation.inc_class_quotient [lemma, in set4]
Relation.inc_coarse_all_equivalence_relations [lemma, in set4]
Relation.inc_in_quotient_substrate [lemma, in set4]
Relation.inc_itself_class [lemma, in set4]
Relation.inc_pr1_substrate [lemma, in set4]
Relation.inc_pr2_substrate [lemma, in set4]
Relation.inc_quotient [lemma, in set4]
Relation.inc_rep_itself [lemma, in set4]
Relation.inc_rep_substrate [lemma, in set4]
Relation.inc_substrate [lemma, in set4]
Relation.inc_substrate_rw [lemma, in set4]
Relation.induced_relation [definition, in set4]
Relation.induced_rel_axioms [definition, in set4]
Relation.induced_rel_class [lemma, in set4]
Relation.induced_rel_equivalence [lemma, in set4]
Relation.induced_rel_iirel_axioms [lemma, in set4]
Relation.induced_rel_related [lemma, in set4]
Relation.induced_rel_substrate [lemma, in set4]
Relation.inter2_is_graph1 [lemma, in set4]
Relation.inter2_is_graph2 [lemma, in set4]
Relation.inter_rel_equivalence [lemma, in set4]
Relation.inter_rel_graph [lemma, in set4]
Relation.inter_rel_reflexive [lemma, in set4]
Relation.inter_rel_rw [lemma, in set4]
Relation.inter_rel_substrate [lemma, in set4]
Relation.inter_rel_symmetric [lemma, in set4]
Relation.inter_rel_transitive [lemma, in set4]
Relation.inverse_direct_value [definition, in set4]
Relation.inv_image_relation [definition, in set4]
Relation.in_class_related [lemma, in set4]
Relation.in_same_coset [definition, in set4]
Relation.isc_equivalence [lemma, in set4]
Relation.isc_reflexive [lemma, in set4]
Relation.isc_symmetric [lemma, in set4]
Relation.isc_transitive [lemma, in set4]
Relation.is_class [definition, in set4]
Relation.is_class_class [lemma, in set4]
Relation.is_class_pr [lemma, in set4]
Relation.is_class_rw [lemma, in set4]
Relation.is_equivalence [definition, in set4]
Relation.is_graph_of [definition, in set4]
Relation.is_reflexive [definition, in set4]
Relation.is_symmetric [definition, in set4]
Relation.is_transitive [definition, in set4]
Relation.nonempty_class_symmetric [lemma, in set4]
Relation.nonempty_image [lemma, in set4]
Relation.non_empty_in_quotient [lemma, in set4]
Relation.partition_class_inc [lemma, in set4]
Relation.partition_from_equivalence [lemma, in set4]
Relation.partition_fun_bijective [lemma, in set4]
Relation.partition_is_equivalence [lemma, in set4]
Relation.partition_relation [definition, in set4]
Relation.partition_relation_class [lemma, in set4]
Relation.partition_relation_class2 [lemma, in set4]
Relation.partition_relation_pr [lemma, in set4]
Relation.partition_relation_substrate [lemma, in set4]
Relation.partition_rel_graph [lemma, in set4]
Relation.prod_of_relation [definition, in set4]
Relation.prod_of_rel_is_rel [lemma, in set4]
Relation.prod_of_rel_pr [lemma, in set4]
Relation.prod_of_rel_refl [lemma, in set4]
Relation.prod_of_rel_sym [lemma, in set4]
Relation.prod_of_rel_trans [lemma, in set4]
Relation.quotient [definition, in set4]
Relation.quotient_canonical_decomposition [lemma, in set4]
Relation.quotient_of_relations [definition, in set4]
Relation.quotient_of_relations_class_bis [lemma, in set4]
Relation.quotient_of_relations_equivalence [lemma, in set4]
Relation.quotient_of_relations_pr [lemma, in set4]
Relation.quotient_of_relations_related [lemma, in set4]
Relation.quotient_of_relations_related_bis [lemma, in set4]
Relation.quotient_of_relations_substrate [lemma, in set4]
Relation.reflexive_ap [lemma, in set4]
Relation.reflexive_ap2 [lemma, in set4]
Relation.reflexive_inc_substrate [lemma, in set4]
Relation.reflexive_r [definition, in set4]
Relation.reflexive_reflexive [lemma, in set4]
Relation.reflexivity_e [lemma, in set4]
Relation.related_class_eq [lemma, in set4]
Relation.related_class_eq1 [lemma, in set4]
Relation.related_ext_to_prod_rel [lemma, in set4]
Relation.related_e_rw [lemma, in set4]
Relation.related_graph_canon_proj [lemma, in set4]
Relation.related_prod_of_rel1 [lemma, in set4]
Relation.related_prod_of_rel2 [lemma, in set4]
Relation.related_rep_class [lemma, in set4]
Relation.related_rep_in_class [lemma, in set4]
Relation.related_rep_rep [lemma, in set4]
Relation.related_rw [lemma, in set4]
Relation.relation_on_quotient [definition, in set4]
Relation.rel_on_quo_pr [lemma, in set4]
Relation.rel_on_quo_pr2 [lemma, in set4]
Relation.representative_system [definition, in set4]
Relation.representative_system_function [definition, in set4]
Relation.rep_sys_function_pr [lemma, in set4]
Relation.rep_sys_function_pr2 [lemma, in set4]
Relation.restricted_eq [definition, in set4]
Relation.right_inv_canon_proj [lemma, in set4]
Relation.saturated [definition, in set4]
Relation.saturated_complement [lemma, in set4]
Relation.saturated_intersection [lemma, in set4]
Relation.saturated_pr [lemma, in set4]
Relation.saturated_pr2 [lemma, in set4]
Relation.saturated_pr3 [lemma, in set4]
Relation.saturated_pr4 [lemma, in set4]
Relation.saturated_union [lemma, in set4]
Relation.saturation_of [definition, in set4]
Relation.saturation_of_pr [lemma, in set4]
Relation.saturation_of_smallest [lemma, in set4]
Relation.saturation_of_union [lemma, in set4]
Relation.section_canon_proj [definition, in set4]
Relation.section_canon_proj_axioms [lemma, in set4]
Relation.section_canon_proj_function [lemma, in set4]
Relation.section_canon_proj_pr [lemma, in set4]
Relation.section_canon_proj_W [lemma, in set4]
Relation.section_is_representative_system_function [lemma, in set4]
Relation.selfinverse_graph_symmetric [lemma, in set4]
Relation.substrate [definition, in set4]
Relation.substrate_for_prod [definition, in set4]
Relation.substrate_prod_of_rel [lemma, in set4]
Relation.substrate_prod_of_rel1 [lemma, in set4]
Relation.substrate_prod_of_rel2 [lemma, in set4]
Relation.substrate_smallest [lemma, in set4]
Relation.substrate_sub [lemma, in set4]
Relation.sub_class_substrate [lemma, in set4]
Relation.sub_graph_coarse_substrate [lemma, in set4]
Relation.sub_im_canon_proj_quotient [lemma, in set4]
Relation.sub_quotient_powerset [lemma, in set4]
Relation.surjective_pr7 [lemma, in set4]
Relation.symmetricity_e [lemma, in set4]
Relation.symmetric_ap [lemma, in set4]
Relation.symmetric_r [definition, in set4]
Relation.symmetric_symmetric [lemma, in set4]
Relation.symmetric_transitive_equivalence [lemma, in set4]
Relation.symmetric_transitive_reflexive [lemma, in set4]
Relation.transitive_ap [lemma, in set4]
Relation.transitive_r [definition, in set4]
Relation.transitive_transitive [lemma, in set4]
Relation.transitivity_e [lemma, in set4]
Relation.trivial_equiv [lemma, in set4]
Relation.union2_is_graph [lemma, in set4]
Relation.union_image [definition, in set4]
Relation.union_quotient [lemma, in set4]
Ro [axiom, in set1]
R_inj [axiom, in set1]
S
set1 [library]set10 [library]
set11 [library]
set2 [library]
set3 [library]
set4 [library]
set5 [library]
set6 [library]
set7 [library]
set8 [library]
set9 [library]
T
Tactics1 [module, in set1]Tactics1.seq_deconj [lemma, in set1]
Tactics1.uneq [lemma, in set1]
Tactics1.uneq2 [lemma, in set1]
U
Union [module, in set1]Union.inc_tack_on_sub [lemma, in set1]
Union.inc_tack_on_x [lemma, in set1]
Union.inc_tack_on_y [lemma, in set1]
Union.inc_union2_rw [lemma, in set1]
Union.sub_union [lemma, in set1]
Union.tack_on [definition, in set1]
Union.tack_on_complement [lemma, in set1]
Union.tack_on_inc [lemma, in set1]
Union.tack_on_or [lemma, in set1]
Union.tack_on_sub [lemma, in set1]
Union.tack_on_when_inc [lemma, in set1]
Union.union [definition, in set1]
Union.union2 [definition, in set1]
Union.union2comm [lemma, in set1]
Union.union2idem [lemma, in set1]
Union.union2sub_first [lemma, in set1]
Union.union2sub_second [lemma, in set1]
Union.union2_first [lemma, in set1]
Union.union2_or [lemma, in set1]
Union.union2_second [lemma, in set1]
Union.union2_sub [lemma, in set1]
Union.union_exists [lemma, in set1]
Union.union_inc [lemma, in set1]
Union.Union_integral [inductive, in set1]
Union.union_sub [lemma, in set1]
W
Worder [module, in set6]Worder.bij_pair_isomorphism_onto_segment [lemma, in set6]
Worder.canonical_doubleton_order [definition, in set6]
Worder.canonical_doubleton_order_pr [lemma, in set6]
Worder.coarse_segment_monotone [lemma, in set6]
Worder.common_extension_order [definition, in set6]
Worder.common_extension_order_axiom [definition, in set6]
Worder.common_ordering_set [definition, in set6]
Worder.common_worder_axiom [definition, in set6]
Worder.compose_order_isomorphism [lemma, in set6]
Worder.compose_order_morphism [lemma, in set6]
Worder.disjoint_union2_rw [lemma, in set6]
Worder.disjoint_union2_rw1 [lemma, in set6]
Worder.empty_is_segment [lemma, in set6]
Worder.identity_isomorphism [lemma, in set6]
Worder.identity_morphism [lemma, in set6]
Worder.increasing_function_segments [lemma, in set6]
Worder.inc_bound_segmentc [lemma, in set6]
Worder.inc_lt1_substrate [lemma, in set6]
Worder.inc_lt2_substrate [lemma, in set6]
Worder.inc_segment [lemma, in set6]
Worder.inc_set_of_segments [lemma, in set6]
Worder.induced_order_trans [lemma, in set6]
Worder.induced_trans [lemma, in set6]
Worder.inductive_graphs [lemma, in set6]
Worder.inductive_max_greater [lemma, in set6]
Worder.inductive_powerset [lemma, in set6]
Worder.inductive_set [definition, in set6]
Worder.intersection_is_segment [lemma, in set6]
Worder.inverse_order_isomorphism [lemma, in set6]
Worder.isomorphic_subset_segment [lemma, in set6]
Worder.isomorphism_worder [lemma, in set6]
Worder.isomorphism_worder_unique [lemma, in set6]
Worder.is_segment [definition, in set6]
Worder.lexicographic_order [definition, in set6]
Worder.lexicographic_order_axioms [definition, in set6]
Worder.lexicographic_order_r [definition, in set6]
Worder.lexorder_gle [lemma, in set6]
Worder.lexorder_order [lemma, in set6]
Worder.lexorder_substrate [lemma, in set6]
Worder.lexorder_substrate_aux [lemma, in set6]
Worder.lexorder_total [lemma, in set6]
Worder.le_in_segment [lemma, in set6]
Worder.lt_in_segment [lemma, in set6]
Worder.maximal_in_powerset [lemma, in set6]
Worder.minimal_in_powerset [lemma, in set6]
Worder.not_in_segment [lemma, in set6]
Worder.not_lt_self [lemma, in set6]
Worder.order_merge1 [lemma, in set6]
Worder.order_merge2 [lemma, in set6]
Worder.order_merge3 [lemma, in set6]
Worder.order_merge4 [lemma, in set6]
Worder.order_merge5 [lemma, in set6]
Worder.order_morphism_pr1 [lemma, in set6]
Worder.restriction_to_segment [definition, in set6]
Worder.restriction_to_segment_axiom [definition, in set6]
Worder.rts_extensionality [lemma, in set6]
Worder.rts_function [lemma, in set6]
Worder.rts_surjective [lemma, in set6]
Worder.rts_W [lemma, in set6]
Worder.segment [definition, in set6]
Worder.segmentc_rw [lemma, in set6]
Worder.segment_alt [lemma, in set6]
Worder.segment_alt1 [lemma, in set6]
Worder.segment_c [definition, in set6]
Worder.segment_c_pr [lemma, in set6]
Worder.segment_dichot_sub [lemma, in set6]
Worder.segment_inc [lemma, in set6]
Worder.segment_induced [lemma, in set6]
Worder.segment_induced1 [lemma, in set6]
Worder.segment_induced_a [lemma, in set6]
Worder.segment_injective [lemma, in set6]
Worder.segment_injective1 [lemma, in set6]
Worder.segment_is_segment [lemma, in set6]
Worder.segment_monotone [lemma, in set6]
Worder.segment_rw [lemma, in set6]
Worder.set_of_segments [definition, in set6]
Worder.set_of_segments_axiom [lemma, in set6]
Worder.set_of_segments_iso [definition, in set6]
Worder.set_of_segments_iso_bijective [lemma, in set6]
Worder.set_of_segments_iso_isomorphism [lemma, in set6]
Worder.set_of_segments_strict [definition, in set6]
Worder.set_of_segments_worder [lemma, in set6]
Worder.singleton_emptyset_not_empty [lemma, in set6]
Worder.singleton_pr1 [lemma, in set6]
Worder.strict_increasing_extens [lemma, in set6]
Worder.subsegment_is_segment [lemma, in set6]
Worder.substrate_canonical_doubleton_order [lemma, in set6]
Worder.substrate_is_segment [lemma, in set6]
Worder.sub_segment [lemma, in set6]
Worder.sub_segmentc [lemma, in set6]
Worder.sub_segment1 [lemma, in set6]
Worder.sub_segment2 [lemma, in set6]
Worder.sub_set_of_segments [lemma, in set6]
Worder.tack_on_segment [lemma, in set6]
Worder.transfinite_aux1 [lemma, in set6]
Worder.transfinite_aux2 [lemma, in set6]
Worder.transfinite_aux3 [lemma, in set6]
Worder.transfinite_def [definition, in set6]
Worder.transfinite_defined [definition, in set6]
Worder.transfinite_defined_pr [lemma, in set6]
Worder.transfinite_definition [lemma, in set6]
Worder.transfinite_definition_stable [lemma, in set6]
Worder.transfinite_pr [lemma, in set6]
Worder.transfinite_principle [lemma, in set6]
Worder.transfinite_principle1 [lemma, in set6]
Worder.transfinite_principle2 [lemma, in set6]
Worder.transfinite_principle_bis [lemma, in set6]
Worder.transfinite_unique [lemma, in set6]
Worder.transfinite_unique1 [lemma, in set6]
Worder.unionf_is_segment [lemma, in set6]
Worder.union_is_segment [lemma, in set6]
Worder.union_segments [lemma, in set6]
Worder.unique_isomorphism_onto_segment [lemma, in set6]
Worder.well_ordered_segment [lemma, in set6]
Worder.worder [definition, in set6]
Worder.wordering_pr [lemma, in set6]
Worder.worder_adjoin_greatest [lemma, in set6]
Worder.worder_canonical_doubleton_order [lemma, in set6]
Worder.worder_hassup [lemma, in set6]
Worder.worder_least [lemma, in set6]
Worder.worder_merge [lemma, in set6]
Worder.worder_r [definition, in set6]
Worder.worder_restriction [lemma, in set6]
Worder.worder_total [lemma, in set6]
Worder.Zermelo [lemma, in set6]
Worder.Zermelo_aux [lemma, in set6]
Worder.Zermelo_aux0 [lemma, in set6]
Worder.Zermelo_aux1 [lemma, in set6]
Worder.Zermelo_aux2 [lemma, in set6]
Worder.Zermelo_aux3 [lemma, in set6]
Worder.Zermelo_aux4 [lemma, in set6]
Worder.Zermelo_axioms [definition, in set6]
Worder.Zermelo_bis [lemma, in set6]
Worder.Zorn_aux [lemma, in set6]
Worder.Zorn_lemma [lemma, in set6]
Axiom Index
A
axiom_of_pair [in set1]C
chooseT [in set1]chooseT_pr [in set1]
E
excluded_middle [in set1]extensionality [in set1]
I
iff_eq [in set1]IM [in set1]
IM_exists [in set1]
IM_inc [in set1]
P
pair_constructor [in set1]prod_extensionality [in set1]
R
Ro [in set1]R_inj [in set1]
Lemma Index
A
Axioms.arrow_extensionality [in set1]Axioms.equal_or_not [in set1]
Axioms.inc_or_not [in set1]
Axioms.p_or_not_p [in set1]
B
Bfunction.acreate_bijective [in set2]Bfunction.acreate_fgraph [in set2]
Bfunction.acreate_function [in set2]
Bfunction.acreate_injective [in set2]
Bfunction.acreate_source [in set2]
Bfunction.acreate_surjective [in set2]
Bfunction.acreate_target [in set2]
Bfunction.acreate_W [in set2]
Bfunction.agrees_same_restriction [in set2]
Bfunction.agrees_same_restrictionC [in set2]
Bfunction.bcreate1_bijective [in set2]
Bfunction.bcreate1_injective [in set2]
Bfunction.bcreate1_surjective [in set2]
Bfunction.bcreate_bijective [in set2]
Bfunction.bcreate_eq [in set2]
Bfunction.bcreate_injective [in set2]
Bfunction.bcreate_inv1 [in set2]
Bfunction.bcreate_inv2 [in set2]
Bfunction.bcreate_inv3 [in set2]
Bfunction.bcreate_surjective [in set2]
Bfunction.bijectiveC_pr [in set2]
Bfunction.bijective_double_inverseC [in set2]
Bfunction.bijective_double_inverseC1 [in set2]
Bfunction.bijective_ext_to_prod2C [in set2]
Bfunction.bijective_from_compose [in set2]
Bfunction.bijective_inverseC [in set2]
Bfunction.bijective_inv_aux [in set2]
Bfunction.bijective_inv_function [in set2]
Bfunction.bijective_pr [in set2]
Bfunction.bijective_source_aux [in set2]
Bfunction.bijective_target_aux [in set2]
Bfunction.bij_is_function [in set2]
Bfunction.bij_left_compose [in set2]
Bfunction.bij_left_inverse [in set2]
Bfunction.bij_left_inverseC [in set2]
Bfunction.bij_right_compose [in set2]
Bfunction.bij_right_inverse [in set2]
Bfunction.bij_right_inverseC [in set2]
Bfunction.bl_bijective [in set2]
Bfunction.bl_function [in set2]
Bfunction.bl_graph1 [in set2]
Bfunction.bl_graph2 [in set2]
Bfunction.bl_graph3 [in set2]
Bfunction.bl_graph4 [in set2]
Bfunction.bl_injective [in set2]
Bfunction.bl_recovers [in set2]
Bfunction.bl_source [in set2]
Bfunction.bl_surjective [in set2]
Bfunction.bl_target [in set2]
Bfunction.bl_W [in set2]
Bfunction.bourbaki_ex5_17 [in set2]
Bfunction.canonical_decomposition1 [in set2]
Bfunction.canonical_decomposition1C [in set2]
Bfunction.ci_function [in set2]
Bfunction.ci_injective [in set2]
Bfunction.ci_range [in set2]
Bfunction.ci_W [in set2]
Bfunction.composable_acreate [in set2]
Bfunction.composable_ext_to_prod2 [in set2]
Bfunction.composable_f_inv [in set2]
Bfunction.composable_inv_f [in set2]
Bfunction.composable_pr [in set2]
Bfunction.composable_pr1 [in set2]
Bfunction.composeC_bij [in set2]
Bfunction.composeC_inj [in set2]
Bfunction.composeC_surj [in set2]
Bfunction.compose_acreate [in set2]
Bfunction.compose_assoc [in set2]
Bfunction.compose_bijective [in set2]
Bfunction.compose_domain [in set2]
Bfunction.compose_ext_to_prod2 [in set2]
Bfunction.compose_ext_to_prod2C [in set2]
Bfunction.compose_function [in set2]
Bfunction.compose_id_left [in set2]
Bfunction.compose_id_leftC [in set2]
Bfunction.compose_id_right [in set2]
Bfunction.compose_id_rightC [in set2]
Bfunction.compose_injective [in set2]
Bfunction.compose_source [in set2]
Bfunction.compose_surjective [in set2]
Bfunction.compose_target [in set2]
Bfunction.compose_W [in set2]
Bfunction.compositionC_associative [in set2]
Bfunction.constant_constant_fun [in set2]
Bfunction.constant_function_fun [in set2]
Bfunction.constant_function_pr [in set2]
Bfunction.constant_function_prop2 [in set2]
Bfunction.constant_fun_constantC [in set2]
Bfunction.constant_fun_pr [in set2]
Bfunction.constant_fun_prC [in set2]
Bfunction.constant_graph [in set2]
Bfunction.constant_source [in set2]
Bfunction.constant_target [in set2]
Bfunction.constant_W [in set2]
Bfunction.corresp_functionT_prop [in set2]
Bfunction.defined_lemT [in set2]
Bfunction.diag_app_function [in set2]
Bfunction.diag_app_range [in set2]
Bfunction.diag_app_W [in set2]
Bfunction.direct_inv_im [in set2]
Bfunction.direct_inv_im_surjective [in set2]
Bfunction.domain_IM [in set2]
Bfunction.empty_function_function [in set2]
Bfunction.empty_function_graph [in set2]
Bfunction.empty_function_prop [in set2]
Bfunction.equipotentC [in set2]
Bfunction.equipotent_prod_singleton [in set2]
Bfunction.equipotent_reflexive [in set2]
Bfunction.equipotent_symmetric [in set2]
Bfunction.equipotent_transitive [in set2]
Bfunction.exists_left_composable [in set2]
Bfunction.exists_left_composableC [in set2]
Bfunction.exists_left_composable_aux [in set2]
Bfunction.exists_left_composable_auxC [in set2]
Bfunction.exists_left_inv_from_inj [in set2]
Bfunction.exists_left_inv_from_injC [in set2]
Bfunction.exists_right_composable [in set2]
Bfunction.exists_right_composableC [in set2]
Bfunction.exists_right_composable_aux [in set2]
Bfunction.exists_right_composable_auxC [in set2]
Bfunction.exists_right_composable_unique [in set2]
Bfunction.exists_right_composable_uniqueC [in set2]
Bfunction.exists_right_inv_from_surj [in set2]
Bfunction.exists_right_inv_from_surjC [in set2]
Bfunction.exists_unique_left_composable [in set2]
Bfunction.exists_unique_left_composableC [in set2]
Bfunction.extendsC_pr [in set2]
Bfunction.ext_to_prod_bijective [in set2]
Bfunction.ext_to_prod_function [in set2]
Bfunction.ext_to_prod_injective [in set2]
Bfunction.ext_to_prod_inverse [in set2]
Bfunction.ext_to_prod_prop [in set2]
Bfunction.ext_to_prod_propJ [in set2]
Bfunction.ext_to_prod_propP [in set2]
Bfunction.ext_to_prod_propQ [in set2]
Bfunction.ext_to_prod_range [in set2]
Bfunction.ext_to_prod_surjective [in set2]
Bfunction.ext_to_prod_W [in set2]
Bfunction.ext_to_prod_W2 [in set2]
Bfunction.first_proj_function [in set2]
Bfunction.first_proj_injective [in set2]
Bfunction.first_proj_surjective [in set2]
Bfunction.first_proj_W [in set2]
Bfunction.function_exten [in set2]
Bfunction.function_extends_restC [in set2]
Bfunction.function_extends_restr [in set2]
Bfunction.function_exten1 [in set2]
Bfunction.function_exten2 [in set2]
Bfunction.function_exten3 [in set2]
Bfunction.function_exten4 [in set2]
Bfunction.function_fgraph [in set2]
Bfunction.function_graph [in set2]
Bfunction.function_rest_of_prolongation [in set2]
Bfunction.f_domain_graph [in set2]
Bfunction.f_range_graph [in set2]
Bfunction.graph_T [in set2]
Bfunction.identityC_bijective [in set2]
Bfunction.identity_bijective [in set2]
Bfunction.identity_function [in set2]
Bfunction.identity_prop [in set2]
Bfunction.identity_prop2 [in set2]
Bfunction.identity_W [in set2]
Bfunction.imageC_exists [in set2]
Bfunction.imageC_inc [in set2]
Bfunction.image_by_fun_source [in set2]
Bfunction.image_of_fun_pr [in set2]
Bfunction.image_singleton [in set2]
Bfunction.inclusionC_compose [in set2]
Bfunction.inclusionC_identity [in set2]
Bfunction.inclusionC_injective [in set2]
Bfunction.inclusionC_pr [in set2]
Bfunction.inc_graph_restriction2 [in set2]
Bfunction.inc_pr1graph_source [in set2]
Bfunction.inc_pr1graph_source1 [in set2]
Bfunction.inc_pr2graph_target [in set2]
Bfunction.inc_pr2graph_target1 [in set2]
Bfunction.inc_W_range_graph [in set2]
Bfunction.inc_W_target [in set2]
Bfunction.inc_W_targetT [in set2]
Bfunction.injective_diag_app [in set2]
Bfunction.injective_ext_to_prod2C [in set2]
Bfunction.injective_pr [in set2]
Bfunction.injective_pr3 [in set2]
Bfunction.injective_pr_bis [in set2]
Bfunction.inj_if_exists_left_inv [in set2]
Bfunction.inj_if_exists_left_invC [in set2]
Bfunction.inj_is_function [in set2]
Bfunction.inj_left_compose2 [in set2]
Bfunction.inj_left_compose2C [in set2]
Bfunction.inj_right_compose [in set2]
Bfunction.inj_right_composeC [in set2]
Bfunction.inverseC_pra [in set2]
Bfunction.inverseC_prb [in set2]
Bfunction.inverseC_prc [in set2]
Bfunction.inverse_bij_is_bij [in set2]
Bfunction.inverse_bij_is_bij1 [in set2]
Bfunction.inverse_direct_image [in set2]
Bfunction.inverse_direct_image_inj [in set2]
Bfunction.inverse_ext_to_prod2C [in set2]
Bfunction.inverse_fun_involutiveC [in set2]
Bfunction.inv_function_bijective [in set2]
Bfunction.inv_graph_canon_bijective [in set2]
Bfunction.inv_graph_canon_function [in set2]
Bfunction.inv_graph_canon_W [in set2]
Bfunction.inv_image_complement [in set2]
Bfunction.in_graph_W [in set2]
Bfunction.is_functional [in set2]
Bfunction.is_function_functional [in set2]
Bfunction.is_function_pr [in set2]
Bfunction.left_composable_value [in set2]
Bfunction.left_composable_valueC [in set2]
Bfunction.left_inverseC_pr [in set2]
Bfunction.left_inverse_composable [in set2]
Bfunction.left_inverse_compose [in set2]
Bfunction.left_inverse_composeC [in set2]
Bfunction.left_inverse_comp_id [in set2]
Bfunction.left_inverse_from_right [in set2]
Bfunction.left_inverse_from_rightC [in set2]
Bfunction.left_inverse_surjective [in set2]
Bfunction.left_inverse_surjectiveC [in set2]
Bfunction.left_inv_compose_rf [in set2]
Bfunction.left_inv_compose_rfC [in set2]
Bfunction.left_inv_compose_rf2 [in set2]
Bfunction.left_inv_compose_rf2C [in set2]
Bfunction.partial_fun1_axioms [in set2]
Bfunction.partial_fun1_function [in set2]
Bfunction.partial_fun1_W [in set2]
Bfunction.partial_fun2_axioms [in set2]
Bfunction.partial_fun2_function [in set2]
Bfunction.partial_fun2_W [in set2]
Bfunction.prC_prop [in set2]
Bfunction.prJ_prop [in set2]
Bfunction.prJ_recov [in set2]
Bfunction.prop_acreate [in set2]
Bfunction.prop_bcreate1 [in set2]
Bfunction.prop_bcreate2 [in set2]
Bfunction.pr1C_prop [in set2]
Bfunction.pr2C_prop [in set2]
Bfunction.range_inc_rw [in set2]
Bfunction.related_inc_source [in set2]
Bfunction.restriction1_bijective [in set2]
Bfunction.restriction1_function [in set2]
Bfunction.restriction1_pr [in set2]
Bfunction.restriction1_surjective [in set2]
Bfunction.restriction1_W [in set2]
Bfunction.restriction2C_pr [in set2]
Bfunction.restriction2C_pr1 [in set2]
Bfunction.restriction2_function [in set2]
Bfunction.restriction2_graph [in set2]
Bfunction.restriction2_injective [in set2]
Bfunction.restriction2_props [in set2]
Bfunction.restriction2_surjective [in set2]
Bfunction.restriction2_W [in set2]
Bfunction.restriction_function [in set2]
Bfunction.restriction_graph1 [in set2]
Bfunction.restriction_recovers [in set2]
Bfunction.restriction_to_image_pr [in set2]
Bfunction.restriction_W [in set2]
Bfunction.restr_domain2 [in set2]
Bfunction.restr_range [in set2]
Bfunction.right_composable_value [in set2]
Bfunction.right_composable_valueC [in set2]
Bfunction.right_inverse_composable [in set2]
Bfunction.right_inverse_compose [in set2]
Bfunction.right_inverse_composeC [in set2]
Bfunction.right_inverse_comp_id [in set2]
Bfunction.right_inverse_from_left [in set2]
Bfunction.right_inverse_from_leftC [in set2]
Bfunction.right_inverse_injective [in set2]
Bfunction.right_inverse_injectiveC [in set2]
Bfunction.right_inverse_pr [in set2]
Bfunction.right_inv_compose_rf [in set2]
Bfunction.right_inv_compose_rfC [in set2]
Bfunction.right_inv_compose_rf2 [in set2]
Bfunction.right_inv_compose_rf2C [in set2]
Bfunction.same_graph_agrees [in set2]
Bfunction.second_proj_function [in set2]
Bfunction.second_proj_surjective [in set2]
Bfunction.second_proj_W [in set2]
Bfunction.section_unique [in set2]
Bfunction.section_uniqueC [in set2]
Bfunction.source_extends [in set2]
Bfunction.source_right_inverse [in set2]
Bfunction.source_T [in set2]
Bfunction.special_empty_function [in set2]
Bfunction.sub_function [in set2]
Bfunction.sub_image_target [in set2]
Bfunction.sub_image_targetC [in set2]
Bfunction.sub_image_target1 [in set2]
Bfunction.sub_inv_im_source [in set2]
Bfunction.surjective_ext_to_prod2C [in set2]
Bfunction.surjective_pr [in set2]
Bfunction.surjective_pr2 [in set2]
Bfunction.surjective_pr3 [in set2]
Bfunction.surjective_pr4 [in set2]
Bfunction.surjective_pr5 [in set2]
Bfunction.surjective_pr6 [in set2]
Bfunction.surj_if_exists_right_inv [in set2]
Bfunction.surj_if_exists_right_invC [in set2]
Bfunction.surj_is_function [in set2]
Bfunction.surj_left_compose [in set2]
Bfunction.surj_left_composeC [in set2]
Bfunction.surj_left_compose2 [in set2]
Bfunction.surj_left_compose2C [in set2]
Bfunction.tack_on_corresp [in set2]
Bfunction.tack_on_function [in set2]
Bfunction.tack_on_f_injective [in set2]
Bfunction.tack_on_surjective [in set2]
Bfunction.tack_on_W_in [in set2]
Bfunction.tack_on_W_out [in set2]
Bfunction.target_left_inverse [in set2]
Bfunction.target_T [in set2]
Bfunction.w_constant_functionC [in set2]
Bfunction.W_extends [in set2]
Bfunction.W_image [in set2]
Bfunction.W_inverse [in set2]
Bfunction.W_inverse2 [in set2]
Bfunction.W_inverse3 [in set2]
Bfunction.W_left_inverse [in set2]
Bfunction.w_left_inverse [in set2]
Bfunction.W_mapping [in set2]
Bfunction.W_pr [in set2]
Bfunction.W_pr2 [in set2]
Bfunction.W_pr3 [in set2]
Bfunction.w_right_inverse [in set2]
Bfunction.W_right_inverse [in set2]
Border.adjoin_greatest [in set5]
Border.axioms_of_order [in set5]
Border.bounded_above_sub [in set5]
Border.bounded_below_sub [in set5]
Border.bounded_both_sub [in set5]
Border.coarser_order [in set5]
Border.coarser_preorder_order [in set5]
Border.coarser_preorder_related [in set5]
Border.coarser_preorder_related1 [in set5]
Border.coarser_preorder_substrate [in set5]
Border.coarser_related [in set5]
Border.coarser_related_bis [in set5]
Border.coarser_substrate [in set5]
Border.cofinal_right_directed [in set5]
Border.coinitial_left_directed [in set5]
Border.compare_inf_sup1 [in set5]
Border.compare_inf_sup2 [in set5]
Border.compatible_equivalence_preorder [in set5]
Border.compatible_equivalence_preorder1 [in set5]
Border.compatible_equivalence_pre_order [in set5]
Border.complementary_decreasing [in set5]
Border.compose3_related [in set5]
Border.constant_fun_decreasing [in set5]
Border.constant_fun_increasing [in set5]
Border.cst_graph_pr [in set5]
Border.decreasing_composition [in set5]
Border.decreasing_fun_from_strict [in set5]
Border.decreasing_fun_reva [in set5]
Border.decreasing_fun_revb [in set5]
Border.diagonal_order [in set5]
Border.emptyset_is_least [in set5]
Border.empty_function_tg_function [in set5]
Border.empty_interval [in set5]
Border.equality_is_order [in set5]
Border.equivalence_preorder [in set5]
Border.equivalence_preorder1 [in set5]
Border.exists_greatest_cofinal [in set5]
Border.exists_least_coinitial [in set5]
Border.extends_in_prop [in set5]
Border.extension_is_order [in set5]
Border.extension_order_pr [in set5]
Border.extension_order_pr1 [in set5]
Border.extension_order_pr2 [in set5]
Border.extension_order_rw [in set5]
Border.function_order_isomorphism [in set5]
Border.function_order_order [in set5]
Border.function_order_pr [in set5]
Border.function_order_reflexive [in set5]
Border.function_order_substrate [in set5]
Border.ggt_inva [in set5]
Border.ggt_invb [in set5]
Border.glt_inva [in set5]
Border.gop_axioms [in set5]
Border.gop_morphism [in set5]
Border.gop_W [in set5]
Border.graph_of_function_axioms [in set5]
Border.graph_of_function_bijective [in set5]
Border.graph_of_function_fonction [in set5]
Border.graph_of_function_isomorphism [in set5]
Border.graph_of_function_sub [in set5]
Border.graph_of_function_W [in set5]
Border.graph_on_rw3 [in set5]
Border.graph_order_order [in set5]
Border.graph_order_pr [in set5]
Border.graph_order_pr1 [in set5]
Border.graph_order_r_pr [in set5]
Border.graph_order_substrate [in set5]
Border.greater_upper_bound [in set5]
Border.greatest_element_pr [in set5]
Border.greatest_induced [in set5]
Border.greatest_is_sup [in set5]
Border.greatest_is_union [in set5]
Border.greatest_lower_bound_doubleton [in set5]
Border.greatest_lower_bound_emptyset [in set5]
Border.greatest_lower_bound_pr [in set5]
Border.greatest_maximal [in set5]
Border.greatest_prolongation [in set5]
Border.greatest_reverse [in set5]
Border.greatest_right_directed [in set5]
Border.greatest_unique_maximal [in set5]
Border.identity_increasing_decreasing [in set5]
Border.inclusion_is_order [in set5]
Border.inclusion_order_rw [in set5]
Border.increasing_fun_from_strict [in set5]
Border.increasing_fun_reva [in set5]
Border.increasing_fun_revb [in set5]
Border.inc_infimum_substrate [in set5]
Border.inc_supremum_substrate [in set5]
Border.induced_order_substrate [in set5]
Border.infimum_pr [in set5]
Border.infimum_pr1 [in set5]
Border.infimum_pr2 [in set5]
Border.infimum_unique [in set5]
Border.inf_comparable [in set5]
Border.inf_comparable1 [in set5]
Border.inf_decreasing [in set5]
Border.inf_decreasing1 [in set5]
Border.inf_distributive [in set5]
Border.inf_distributive1 [in set5]
Border.inf_distributive2 [in set5]
Border.inf_distributive3 [in set5]
Border.inf_inclusion [in set5]
Border.inf_increasing2 [in set5]
Border.inf_induced1 [in set5]
Border.inf_induced2 [in set5]
Border.inf_in_product [in set5]
Border.inf_in_total_order [in set5]
Border.inf_pr [in set5]
Border.inf_sup_opp [in set5]
Border.intersection4 [in set5]
Border.intersection_interval [in set5]
Border.intersection_is_inf [in set5]
Border.intersection_is_inf1 [in set5]
Border.intersection_is_least [in set5]
Border.intersection_i1 [in set5]
Border.intersection_i2 [in set5]
Border.intersection_i3 [in set5]
Border.inter_rel_order [in set5]
Border.is_inf_fun_pr [in set5]
Border.is_inf_graph_pr [in set5]
Border.is_inf_graph_pr1 [in set5]
Border.is_sup_fun_pr [in set5]
Border.is_sup_graph_pr [in set5]
Border.is_sup_graph_pr1 [in set5]
Border.largest_partition_is_largest [in set5]
Border.lattice_directed [in set5]
Border.lattice_inf_pr [in set5]
Border.lattice_inverse [in set5]
Border.lattice_sup_pr [in set5]
Border.least_element_pr [in set5]
Border.least_equivalence [in set5]
Border.least_induced [in set5]
Border.least_is_inf [in set5]
Border.least_is_intersection [in set5]
Border.least_left_directed [in set5]
Border.least_minimal [in set5]
Border.least_not_greatest [in set5]
Border.least_prolongation [in set5]
Border.least_reverse [in set5]
Border.least_unique_minimal [in set5]
Border.least_upper_bound_doubleton [in set5]
Border.least_upper_bound_emptyset [in set5]
Border.least_upper_bound_pr [in set5]
Border.left_directed_mimimal [in set5]
Border.left_directed_pr [in set5]
Border.leq_lt_trans [in set5]
Border.le_pr [in set5]
Border.lt_leq_trans [in set5]
Border.lt_lt_trans [in set5]
Border.maximal_element_opp [in set5]
Border.maximal_opposite [in set5]
Border.maximal_prolongation [in set5]
Border.minimal_element_opp [in set5]
Border.minimal_inclusion [in set5]
Border.monotone_fun_reva [in set5]
Border.monotone_fun_revb [in set5]
Border.nondisjoint [in set5]
Border.nonempty_closed_interval [in set5]
Border.not_le_gt [in set5]
Border.opposite_gge [in set5]
Border.opposite_gle [in set5]
Border.opposite_induced [in set5]
Border.opposite_is_order [in set5]
Border.opposite_is_order_r [in set5]
Border.opposite_is_preorder1 [in set5]
Border.opposite_is_preorder_r [in set5]
Border.opposite_left_directed [in set5]
Border.opposite_lower_bound [in set5]
Border.opposite_right_directed [in set5]
Border.opposite_upper_bound [in set5]
Border.order_antisymmetry [in set5]
Border.order_associated_graph [in set5]
Border.order_associated_order [in set5]
Border.order_associated_pr [in set5]
Border.order_associated_related1 [in set5]
Border.order_associated_related2 [in set5]
Border.order_associated_substrate [in set5]
Border.order_from_rel [in set5]
Border.order_from_rel1 [in set5]
Border.order_has_graph [in set5]
Border.order_has_graph0 [in set5]
Border.order_has_graph2 [in set5]
Border.order_if_has_graph [in set5]
Border.order_if_has_graph2 [in set5]
Border.order_induced_order [in set5]
Border.order_isomorphism_increasing [in set5]
Border.order_isomorphism_opposite [in set5]
Border.order_isomorphism_pr [in set5]
Border.order_is_graph [in set5]
Border.order_is_order [in set5]
Border.order_morphism_increasing [in set5]
Border.order_pr [in set5]
Border.order_preorder [in set5]
Border.order_reflexivity [in set5]
Border.order_reflexivity_pr [in set5]
Border.order_symmetricity_pr [in set5]
Border.order_transitivity [in set5]
Border.order_transportation [in set5]
Border.order_with_greatest_pr [in set5]
Border.partition_relation_set_order [in set5]
Border.partition_relation_set_order_antisymmetric [in set5]
Border.partition_relation_set_pr [in set5]
Border.partition_relation_set_pr1 [in set5]
Border.partition_set_in_double_powerset [in set5]
Border.pfs_function [in set5]
Border.pfs_partition [in set5]
Border.pfs_W [in set5]
Border.powerset_lattice [in set5]
Border.preorder_from_rel [in set5]
Border.preorder_graph [in set5]
Border.preorder_induced_order [in set5]
Border.preorder_is_preorder [in set5]
Border.preorder_prop [in set5]
Border.preorder_prop1 [in set5]
Border.preorder_prop2 [in set5]
Border.preorder_reflexivity [in set5]
Border.product2_order_order [in set5]
Border.product2_order_pr [in set5]
Border.product2_order_preorder [in set5]
Border.product2_order_preorder_substrate [in set5]
Border.product2_order_substrate [in set5]
Border.product_lattice [in set5]
Border.product_left_directed [in set5]
Border.product_order_axioms_x [in set5]
Border.product_order_def [in set5]
Border.product_order_order [in set5]
Border.product_order_related [in set5]
Border.product_order_substrate [in set5]
Border.product_right_directed [in set5]
Border.prod_of_substrates_rw [in set5]
Border.prs_is_equivalence [in set5]
Border.reflexive_induced_order [in set5]
Border.related_induced_order [in set5]
Border.related_induced_order1 [in set5]
Border.related_induced_order2 [in set5]
Border.related_induced_order3 [in set5]
Border.related_induced_order4 [in set5]
Border.relation_induced_order [in set5]
Border.right_directed_maximal [in set5]
Border.right_directed_pr [in set5]
Border.set_of_graphs_pr [in set5]
Border.set_of_lower_bounds_emptyset [in set5]
Border.set_of_majorants1_decreasing [in set5]
Border.set_of_majorants1_pr [in set5]
Border.set_of_partition_rw [in set5]
Border.set_of_preorders_rw [in set5]
Border.set_of_upper_bounds_emptyset [in set5]
Border.singleton_bounded [in set5]
Border.singleton_interval [in set5]
Border.singleton_pr [in set5]
Border.smaller_lower_bound [in set5]
Border.smallest_partition_is_smallest [in set5]
Border.strict_decreasing_from_injective [in set5]
Border.strict_decreasing_fun_reva [in set5]
Border.strict_decreasing_fun_revb [in set5]
Border.strict_increasing_from_injective [in set5]
Border.strict_increasing_fun_reva [in set5]
Border.strict_increasing_fun_revb [in set5]
Border.strict_monotone_from_injective [in set5]
Border.strict_monotone_fun_reva [in set5]
Border.strict_monotone_fun_revb [in set5]
Border.subinclusion_is_order [in set5]
Border.subinclusion_order_rw [in set5]
Border.substrate_domain_order [in set5]
Border.substrate_equivalence_associated_o [in set5]
Border.substrate_extension_order [in set5]
Border.substrate_graph_on [in set5]
Border.substrate_inclusion_order [in set5]
Border.substrate_induced_order [in set5]
Border.substrate_induced_order1 [in set5]
Border.substrate_opposite_order [in set5]
Border.substrate_subinclusion_order [in set5]
Border.sub_is_order [in set5]
Border.sub_lower_bound [in set5]
Border.sub_partition_relation_set_coarse [in set5]
Border.sub_upper_bound [in set5]
Border.supremum_pr [in set5]
Border.supremum_pr1 [in set5]
Border.supremum_pr2 [in set5]
Border.supremum_unique [in set5]
Border.sup_comparable [in set5]
Border.sup_comparable1 [in set5]
Border.sup_distributive [in set5]
Border.sup_distributive1 [in set5]
Border.sup_distributive2 [in set5]
Border.sup_distributive3 [in set5]
Border.sup_extension_order1 [in set5]
Border.sup_extension_order2 [in set5]
Border.sup_inclusion [in set5]
Border.sup_increasing [in set5]
Border.sup_increasing1 [in set5]
Border.sup_increasing2 [in set5]
Border.sup_induced1 [in set5]
Border.sup_induced2 [in set5]
Border.sup_inf_opp [in set5]
Border.sup_in_product [in set5]
Border.sup_in_total_order [in set5]
Border.sup_pr [in set5]
Border.the_greatest_element_pr [in set5]
Border.the_greatest_element_pr2 [in set5]
Border.the_greatest_interval [in set5]
Border.the_least_element_pr [in set5]
Border.the_least_element_pr2 [in set5]
Border.the_least_interval [in set5]
Border.the_least_reverse [in set5]
Border.total_order_conterexample [in set5]
Border.total_order_directed [in set5]
Border.total_order_increasing_morphism [in set5]
Border.total_order_lattice [in set5]
Border.total_order_monotone_injective [in set5]
Border.total_order_opposite [in set5]
Border.total_order_pr [in set5]
Border.total_order_pr1 [in set5]
Border.total_order_pr2 [in set5]
Border.total_order_small [in set5]
Border.total_order_sub [in set5]
Border.transitive_induced_order [in set5]
Border.union_is_greatest [in set5]
Border.union_is_sup [in set5]
Border.union_is_sup1 [in set5]
Border.unique_greatest [in set5]
Border.unique_least [in set5]
Border.wholeset_is_greatest [in set5]
Bproduct.cf_injective [in set3]
Bproduct.complementary_intersection1 [in set3]
Bproduct.complementary_union1 [in set3]
Bproduct.compose_V [in set3]
Bproduct.constant_graph_function [in set3]
Bproduct.constant_graph_is_constant [in set3]
Bproduct.constant_graph_small_range [in set3]
Bproduct.constant_graph_V [in set3]
Bproduct.diagonal_graph_rw [in set3]
Bproduct.distrib_inter2_union [in set3]
Bproduct.distrib_inter_prod [in set3]
Bproduct.distrib_inter_prod_inter [in set3]
Bproduct.distrib_inter_union [in set3]
Bproduct.distrib_product2_inter [in set3]
Bproduct.distrib_product2_union [in set3]
Bproduct.distrib_prod2_inter [in set3]
Bproduct.distrib_prod2_union [in set3]
Bproduct.distrib_prod_intersection [in set3]
Bproduct.distrib_prod_inter2_prod [in set3]
Bproduct.distrib_prod_union [in set3]
Bproduct.distrib_union2_inter [in set3]
Bproduct.distrib_union_inter [in set3]
Bproduct.extension_partial_product [in set3]
Bproduct.ext_map_prod_composable [in set3]
Bproduct.ext_map_prod_compose [in set3]
Bproduct.ext_map_prod_function [in set3]
Bproduct.ext_map_prod_injective [in set3]
Bproduct.ext_map_prod_surjective [in set3]
Bproduct.ext_map_prod_taxioms [in set3]
Bproduct.ext_map_prod_W [in set3]
Bproduct.ext_map_prod_WV [in set3]
Bproduct.first_proj_bijective [in set3]
Bproduct.fun_set_to_prod1 [in set3]
Bproduct.fun_set_to_prod2 [in set3]
Bproduct.fun_set_to_prod3 [in set3]
Bproduct.fun_set_to_prod4 [in set3]
Bproduct.fun_set_to_prod6 [in set3]
Bproduct.fun_set_to_prod7 [in set3]
Bproduct.fun_set_to_prod8 [in set3]
Bproduct.gbcreate_domain [in set3]
Bproduct.gbcreate_fgraph [in set3]
Bproduct.gbcreate_graph [in set3]
Bproduct.gbcreate_rw [in set3]
Bproduct.gbcreate_V [in set3]
Bproduct.graphset_pr1 [in set3]
Bproduct.graphset_pr2 [in set3]
Bproduct.graph_exten [in set3]
Bproduct.intersectionf_singleton [in set3]
Bproduct.is_singleton_rw [in set3]
Bproduct.nonempty_from_domain [in set3]
Bproduct.nonempty_product3 [in set3]
Bproduct.pam_axioms [in set3]
Bproduct.pam_bijective [in set3]
Bproduct.pam_function [in set3]
Bproduct.pam_injective [in set3]
Bproduct.pam_W [in set3]
Bproduct.partition_product [in set3]
Bproduct.pc_axioms [in set3]
Bproduct.pc_axioms0 [in set3]
Bproduct.pc_bijective [in set3]
Bproduct.pc_function [in set3]
Bproduct.pc_W [in set3]
Bproduct.pc_WV [in set3]
Bproduct.popc_axioms [in set3]
Bproduct.popc_bijection [in set3]
Bproduct.popc_target [in set3]
Bproduct.popc_target_aux [in set3]
Bproduct.popc_W [in set3]
Bproduct.pri_axioms [in set3]
Bproduct.pri_function [in set3]
Bproduct.pri_surjective [in set3]
Bproduct.pri_W [in set3]
Bproduct.prj_axioms [in set3]
Bproduct.prj_bijective [in set3]
Bproduct.prj_function [in set3]
Bproduct.prj_surjective [in set3]
Bproduct.prj_W [in set3]
Bproduct.prj_WV [in set3]
Bproduct.productb_exten [in set3]
Bproduct.productb_monotone1 [in set3]
Bproduct.productb_monotone2 [in set3]
Bproduct.productb_rw [in set3]
Bproduct.productf_exten [in set3]
Bproduct.productf_extension [in set3]
Bproduct.productf_rw [in set3]
Bproduct.productt_exten [in set3]
Bproduct.productt_nonempty [in set3]
Bproduct.productt_nonempty2 [in set3]
Bproduct.productt_rw [in set3]
Bproduct.product1_canon_axioms [in set3]
Bproduct.product1_canon_bijective [in set3]
Bproduct.product1_canon_function [in set3]
Bproduct.product1_canon_W [in set3]
Bproduct.product1_pr [in set3]
Bproduct.product1_pr2 [in set3]
Bproduct.product1_rw [in set3]
Bproduct.product2_canon_axioms [in set3]
Bproduct.product2_canon_bijective [in set3]
Bproduct.product2_canon_function [in set3]
Bproduct.product2_canon_W [in set3]
Bproduct.product2_rw [in set3]
Bproduct.product2_trivial [in set3]
Bproduct.product_eq_graphset [in set3]
Bproduct.product_nonempty [in set3]
Bproduct.product_nonempty2 [in set3]
Bproduct.product_singleton [in set3]
Bproduct.product_sub_graphset [in set3]
Bproduct.product_trivial [in set3]
Bproduct.prod_assoc_map2 [in set3]
Bproduct.prod_of_function_axioms [in set3]
Bproduct.prod_of_function_function [in set3]
Bproduct.prod_of_function_W [in set3]
Bproduct.prod_of_products_fam_pr [in set3]
Bproduct.prod_of_products_function [in set3]
Bproduct.prod_of_products_source [in set3]
Bproduct.prod_of_products_target [in set3]
Bproduct.prod_of_products_W [in set3]
Bproduct.prod_of_prod_inc_target [in set3]
Bproduct.restriction_graph2 [in set3]
Bproduct.trivial_fgraph [in set3]
Bproduct.trivial_product1 [in set3]
Bproduct.unionf_emptyset [in set3]
Bproduct.unionf_singleton [in set3]
Bproduct.variantLc_prop [in set3]
Bproduct.variant_if_not_rw1 [in set3]
Bproduct.variant_if_rw1 [in set3]
Bunion.agrees_on_covering [in set3]
Bunion.coarser_antisymmetric [in set3]
Bunion.coarser_reflexive [in set3]
Bunion.coarser_same [in set3]
Bunion.coarser_transitive [in set3]
Bunion.complementary_intersection [in set3]
Bunion.complementary_union [in set3]
Bunion.composable_for_function [in set3]
Bunion.constant_function_pr [in set3]
Bunion.covering_f_pr [in set3]
Bunion.covering_pr [in set3]
Bunion.c3f_axioms [in set3]
Bunion.c3f_bijective [in set3]
Bunion.c3f_function [in set3]
Bunion.c3f_injective [in set3]
Bunion.c3f_surjective [in set3]
Bunion.c3f_W [in set3]
Bunion.disjoint_complement [in set3]
Bunion.disjoint_pr [in set3]
Bunion.disjoint_symmetric [in set3]
Bunion.disjoint_union_disjoint [in set3]
Bunion.disjoint_union_lemma [in set3]
Bunion.disjoint_union_pr [in set3]
Bunion.empty_set_of_functions_target [in set3]
Bunion.empty_source_graph [in set3]
Bunion.empty_target_graph [in set3]
Bunion.empty_unionf [in set3]
Bunion.empty_unionf1 [in set3]
Bunion.empty_uniont1 [in set3]
Bunion.etp_axioms [in set3]
Bunion.etp_composable [in set3]
Bunion.etp_compose [in set3]
Bunion.etp_function [in set3]
Bunion.etp_identity [in set3]
Bunion.etp_injective [in set3]
Bunion.etp_surjective [in set3]
Bunion.etp_W [in set3]
Bunion.extension_covering [in set3]
Bunion.extension_covering1 [in set3]
Bunion.extension_partition [in set3]
Bunion.extension_partition1 [in set3]
Bunion.fpfa_axioms [in set3]
Bunion.fpfa_bijective [in set3]
Bunion.fpfa_function [in set3]
Bunion.fpfa_W [in set3]
Bunion.fpfb_axioms [in set3]
Bunion.fpfb_function [in set3]
Bunion.fpfb_W [in set3]
Bunion.fpfb_WW [in set3]
Bunion.fpf_axioms [in set3]
Bunion.fpf_function [in set3]
Bunion.fpf_W [in set3]
Bunion.graph_axioms [in set3]
Bunion.graph_bijective [in set3]
Bunion.image_of_covering [in set3]
Bunion.image_of_intersection [in set3]
Bunion.image_of_intersection2 [in set3]
Bunion.image_of_union [in set3]
Bunion.image_of_union2 [in set3]
Bunion.inc_set_of_gfunctions [in set3]
Bunion.injective_partition [in set3]
Bunion.inj_image_of_comp [in set3]
Bunion.inj_image_of_intersection [in set3]
Bunion.inj_image_of_intersection2 [in set3]
Bunion.intersectionb_empty [in set3]
Bunion.intersectionb_extensionality [in set3]
Bunion.intersectionb_forall [in set3]
Bunion.intersectionb_inc [in set3]
Bunion.intersectionb_rewrite [in set3]
Bunion.intersectionb_rw [in set3]
Bunion.intersectionf_empty [in set3]
Bunion.intersectionf_extensionality [in set3]
Bunion.intersectionf_forall [in set3]
Bunion.intersectionf_inc [in set3]
Bunion.intersectionf_rw [in set3]
Bunion.intersectionf_singleton [in set3]
Bunion.intersectiont_constant [in set3]
Bunion.intersectiont_constant_alt [in set3]
Bunion.intersectiont_empty [in set3]
Bunion.intersectiont_extensionality [in set3]
Bunion.intersectiont_forall [in set3]
Bunion.intersectiont_inc [in set3]
Bunion.intersectiont_rewrite [in set3]
Bunion.intersectiont_rw [in set3]
Bunion.intersectiont_singleton [in set3]
Bunion.intersectiont_sub [in set3]
Bunion.intersectiont_sub2 [in set3]
Bunion.intersection2assoc [in set3]
Bunion.intersection2_comp [in set3]
Bunion.intersection2_complement [in set3]
Bunion.intersection_assoc [in set3]
Bunion.intersection_covering2_pr [in set3]
Bunion.intersection_covering_coarser1 [in set3]
Bunion.intersection_covering_coarser2 [in set3]
Bunion.intersection_covering_coarser3 [in set3]
Bunion.intersection_cov_coarser1 [in set3]
Bunion.intersection_cov_coarser2 [in set3]
Bunion.intersection_cov_coarser3 [in set3]
Bunion.intersection_is_covering [in set3]
Bunion.intersection_monotone [in set3]
Bunion.intersection_monotone2 [in set3]
Bunion.intersection_of_twosets [in set3]
Bunion.intersection_of_twosets_aux [in set3]
Bunion.intersection_prop [in set3]
Bunion.intersection_singleton [in set3]
Bunion.intersection_union_distrib1 [in set3]
Bunion.intersection_union_distrib2 [in set3]
Bunion.inv_image_disjoint [in set3]
Bunion.inv_image_of_comp [in set3]
Bunion.inv_image_of_covering [in set3]
Bunion.inv_image_of_intersection [in set3]
Bunion.inv_image_of_intersection2 [in set3]
Bunion.is_partition_with_complement [in set3]
Bunion.largest_partition_pr [in set3]
Bunion.mutually_disjoint_prop [in set3]
Bunion.mutually_disjoint_prop2 [in set3]
Bunion.nonemptyT_doubleton [in set3]
Bunion.partial_fun_axioms_pr [in set3]
Bunion.partion_union_disjoint [in set3]
Bunion.partitionset_pr [in set3]
Bunion.partitions_is_covering [in set3]
Bunion.partition_fam_is_covering [in set3]
Bunion.partition_fam_partition [in set3]
Bunion.partition_inc_exists [in set3]
Bunion.partition_inc_unique [in set3]
Bunion.partition_largest [in set3]
Bunion.partition_same [in set3]
Bunion.partition_same2 [in set3]
Bunion.partition_smallest [in set3]
Bunion.powerset_emptyset [in set3]
Bunion.powerset_monotone [in set3]
Bunion.product_is_covering2 [in set3]
Bunion.product_of_covering [in set3]
Bunion.set_extens_aux [in set3]
Bunion.set_of_functions_equipotent [in set3]
Bunion.set_of_functions_extens [in set3]
Bunion.set_of_functions_rw [in set3]
Bunion.set_of_gfunctions_inc [in set3]
Bunion.set_of_sub_functions_rw [in set3]
Bunion.singleton_type_inj [in set3]
Bunion.small_set_of_functions_source [in set3]
Bunion.small_set_of_functions_target [in set3]
Bunion.spfa_axioms [in set3]
Bunion.spfa_bijective [in set3]
Bunion.spfa_function [in set3]
Bunion.spfa_W [in set3]
Bunion.spfb_axioms [in set3]
Bunion.spfb_function [in set3]
Bunion.spfb_W [in set3]
Bunion.spfb_WW [in set3]
Bunion.spf_axioms [in set3]
Bunion.spf_function [in set3]
Bunion.spf_W [in set3]
Bunion.sub_covering [in set3]
Bunion.sub_intersectiont [in set3]
Bunion.sub_uniont [in set3]
Bunion.sub_uniont2 [in set3]
Bunion.unionb_alt [in set3]
Bunion.unionb_exists [in set3]
Bunion.unionb_extensionality [in set3]
Bunion.unionb_identity [in set3]
Bunion.unionb_inc [in set3]
Bunion.unionb_rewrite [in set3]
Bunion.unionb_rewrite1 [in set3]
Bunion.unionb_rw [in set3]
Bunion.unionf_exists [in set3]
Bunion.unionf_extensionality [in set3]
Bunion.unionf_inc [in set3]
Bunion.unionf_rw [in set3]
Bunion.unionf_singleton [in set3]
Bunion.uniont_constant [in set3]
Bunion.uniont_constant_alt [in set3]
Bunion.uniont_exists [in set3]
Bunion.uniont_extensionality [in set3]
Bunion.uniont_inc [in set3]
Bunion.uniont_rewrite [in set3]
Bunion.uniont_rw [in set3]
Bunion.uniont_singleton [in set3]
Bunion.uniont_sub [in set3]
Bunion.union2assoc [in set3]
Bunion.union2_comp [in set3]
Bunion.union2_complement [in set3]
Bunion.union_assoc [in set3]
Bunion.union_doubleton [in set3]
Bunion.union_monotone [in set3]
Bunion.union_monotone2 [in set3]
Bunion.union_of_twosets [in set3]
Bunion.union_of_twosets_aux [in set3]
Bunion.union_prop [in set3]
Bunion.union_singleton [in set3]
Bunion.variantLc_domain [in set3]
Bunion.variantLc_domain_nonempty [in set3]
Bunion.variantLc_fgraph [in set3]
Bunion.variant_domain [in set3]
Bunion.variant_fgraph [in set3]
Bunion.variant_if_not_rw [in set3]
Bunion.variant_if_rw [in set3]
Bunion.variant_V_a [in set3]
Bunion.variant_V_b [in set3]
Bunion.variant_V_ca [in set3]
Bunion.variant_V_cb [in set3]
C
Cardinal.cantor [in set7]Cardinal.cantor_bis [in set7]
Cardinal.cardinal0 [in set7]
Cardinal.cardinal1 [in set7]
Cardinal.cardinal2 [in set7]
Cardinal.cardinal_antisymmetry1 [in set7]
Cardinal.cardinal_antisymmetry2 [in set7]
Cardinal.cardinal_cardinal [in set7]
Cardinal.cardinal_distrib_prod2_sum [in set7]
Cardinal.cardinal_distrib_prod_sum [in set7]
Cardinal.cardinal_distrib_prod_sum2 [in set7]
Cardinal.cardinal_distrib_prod_sum3 [in set7]
Cardinal.cardinal_doubleton [in set7]
Cardinal.cardinal_emptyset [in set7]
Cardinal.cardinal_equipotent [in set7]
Cardinal.cardinal_equipotent1 [in set7]
Cardinal.cardinal_le1 [in set7]
Cardinal.cardinal_le2 [in set7]
Cardinal.cardinal_le3 [in set7]
Cardinal.cardinal_le5 [in set7]
Cardinal.cardinal_le7 [in set7]
Cardinal.cardinal_le8 [in set7]
Cardinal.cardinal_le9 [in set7]
Cardinal.cardinal_le_lt_trans [in set7]
Cardinal.cardinal_le_reflexive [in set7]
Cardinal.cardinal_le_total_order [in set7]
Cardinal.cardinal_le_total_order1 [in set7]
Cardinal.cardinal_le_total_order2 [in set7]
Cardinal.cardinal_le_total_order3 [in set7]
Cardinal.cardinal_le_transitive [in set7]
Cardinal.cardinal_le_when_complement [in set7]
Cardinal.cardinal_lt_le_trans [in set7]
Cardinal.cardinal_nonemptyset [in set7]
Cardinal.cardinal_nonemptyset1 [in set7]
Cardinal.cardinal_of_cardinal [in set7]
Cardinal.cardinal_one_is_singleton [in set7]
Cardinal.cardinal_pr [in set7]
Cardinal.cardinal_prod_assoc [in set7]
Cardinal.cardinal_prod_commutative [in set7]
Cardinal.cardinal_prod_pr [in set7]
Cardinal.cardinal_pr0 [in set7]
Cardinal.cardinal_singleton [in set7]
Cardinal.cardinal_sum_assoc [in set7]
Cardinal.cardinal_sum_commutative [in set7]
Cardinal.cardinal_sum_pr [in set7]
Cardinal.cardinal_sum_pr1 [in set7]
Cardinal.cardinal_sum_pr2 [in set7]
Cardinal.cardinal_sum_pr3 [in set7]
Cardinal.cardinal_supremum [in set7]
Cardinal.cardinal_supremum1 [in set7]
Cardinal.cardinal_two_is_doubleton [in set7]
Cardinal.cardinal_zero [in set7]
Cardinal.card_commutative_aux [in set7]
Cardinal.card_le_one_prop [in set7]
Cardinal.card_le_one_prop1 [in set7]
Cardinal.card_le_two_prop [in set7]
Cardinal.card_le_two_prop1 [in set7]
Cardinal.card_mult_associative [in set7]
Cardinal.card_mult_commutative [in set7]
Cardinal.card_mult_is_cardinal [in set7]
Cardinal.card_mult_pr [in set7]
Cardinal.card_mult_pr0 [in set7]
Cardinal.card_mult_pr1 [in set7]
Cardinal.card_mult_pr2 [in set7]
Cardinal.card_one_not_two [in set7]
Cardinal.card_one_not_zero [in set7]
Cardinal.card_plus_associative [in set7]
Cardinal.card_plus_commutative [in set7]
Cardinal.card_plus_is_cardinal [in set7]
Cardinal.card_plus_pr [in set7]
Cardinal.card_plus_pr0 [in set7]
Cardinal.card_plus_pr1 [in set7]
Cardinal.card_plus_pr2 [in set7]
Cardinal.card_powerset [in set7]
Cardinal.card_pow_pr [in set7]
Cardinal.card_pow_pr1 [in set7]
Cardinal.card_pow_pr2 [in set7]
Cardinal.card_pow_pr3 [in set7]
Cardinal.card_two_not_zero [in set7]
Cardinal.card_two_pr [in set7]
Cardinal.disjoint_union2_pr [in set7]
Cardinal.disjoint_union2_pr0 [in set7]
Cardinal.disjoint_union2_pr1 [in set7]
Cardinal.disjoint_union2_pr3 [in set7]
Cardinal.disjoint_union2_pr4 [in set7]
Cardinal.disjoint_with_singleton [in set7]
Cardinal.distrib_inter_prod2 [in set7]
Cardinal.distrib_inter_prod3 [in set7]
Cardinal.distrib_prod2_sum [in set7]
Cardinal.doubleton_equipotent1 [in set7]
Cardinal.doubleton_fam_canon [in set7]
Cardinal.equipotent_a_times_singl [in set7]
Cardinal.equipotent_disjoint_union [in set7]
Cardinal.equipotent_disjoint_union1 [in set7]
Cardinal.equipotent_disjoint_union2 [in set7]
Cardinal.equipotent_product [in set7]
Cardinal.equipotent_productb [in set7]
Cardinal.equipotent_productf [in set7]
Cardinal.equipotent_product1 [in set7]
Cardinal.equipotent_product_sym [in set7]
Cardinal.equipotent_singl_times_a [in set7]
Cardinal.equipotent_to_emptyset [in set7]
Cardinal.image_smaller_cardinal [in set7]
Cardinal.inj_compose1 [in set7]
Cardinal.nonempty_card_ge2 [in set7]
Cardinal.not_card_le_lt [in set7]
Cardinal.one_small_cardinal [in set7]
Cardinal.one_small_cardinal1 [in set7]
Cardinal.one_unit_prod [in set7]
Cardinal.one_unit_prodl [in set7]
Cardinal.one_unit_prodr [in set7]
Cardinal.power_increasing1 [in set7]
Cardinal.power_of_prod [in set7]
Cardinal.power_of_prod2 [in set7]
Cardinal.power_of_prod3 [in set7]
Cardinal.power_of_sum [in set7]
Cardinal.power_of_sum2 [in set7]
Cardinal.power_x_0 [in set7]
Cardinal.power_x_1 [in set7]
Cardinal.power_x_2 [in set7]
Cardinal.power_0_x [in set7]
Cardinal.power_0_0 [in set7]
Cardinal.power_1_x [in set7]
Cardinal.product2associative [in set7]
Cardinal.product_increasing [in set7]
Cardinal.product_increasing1 [in set7]
Cardinal.product_increasing2 [in set7]
Cardinal.product_increasing3 [in set7]
Cardinal.restriction_to_image_axioms [in set7]
Cardinal.restriction_to_image_bijective [in set7]
Cardinal.restriction_to_image_surjective [in set7]
Cardinal.set_of_cardinals_pr [in set7]
Cardinal.set_of_card_two [in set7]
Cardinal.singletons_equipotent [in set7]
Cardinal.sub_smaller [in set7]
Cardinal.succ_injective [in set7]
Cardinal.sum_increasing [in set7]
Cardinal.sum_increasing1 [in set7]
Cardinal.sum_increasing2 [in set7]
Cardinal.sum_increasing3 [in set7]
Cardinal.sum_of_ones [in set7]
Cardinal.sum_of_ones1 [in set7]
Cardinal.sum_of_same [in set7]
Cardinal.sum_of_same1 [in set7]
Cardinal.surjective_cardinal_le [in set7]
Cardinal.trivial_cardinal_prod [in set7]
Cardinal.trivial_cardinal_prod1 [in set7]
Cardinal.trivial_cardinal_sum [in set7]
Cardinal.trivial_cardinal_sum1 [in set7]
Cardinal.trivial_card_plus [in set7]
Cardinal.two_terms_bij [in set7]
Cardinal.wordering_cardinal_le [in set7]
Cardinal.wordering_cardinal_le_pr [in set7]
Cardinal.zero_cardinal_product [in set7]
Cardinal.zero_cardinal_product2 [in set7]
Cardinal.zero_is_emptyset [in set7]
Cardinal.zero_product_absorbing [in set7]
Cardinal.zero_prod_absorbing [in set7]
Cardinal.zero_smallest [in set7]
Cardinal.zero_smallest1 [in set7]
Cardinal.zero_smallest2 [in set7]
Cardinal.zero_unit_sum [in set7]
Cardinal.zero_unit_suml [in set7]
Cardinal.zero_unit_sumr [in set7]
Cartesian.empty_product1 [in set1]
Cartesian.empty_product2 [in set1]
Cartesian.empty_product_pr [in set1]
Cartesian.pair_in_product [in set1]
Cartesian.product_inc [in set1]
Cartesian.product_inc_rw [in set1]
Cartesian.product_monotone [in set1]
Cartesian.product_monotone_left [in set1]
Cartesian.product_monotone_left2 [in set1]
Cartesian.product_monotone_right [in set1]
Cartesian.product_monotone_right2 [in set1]
Cartesian.product_pair_inc [in set1]
Cartesian.product_pair_pr [in set1]
Cartesian.product_pr [in set1]
Complement.complement_emptyset [in set1]
Complement.complement_itself [in set1]
Complement.complement_monotone [in set1]
Complement.double_complement [in set1]
Complement.empty_complement [in set1]
Complement.inc_complement [in set1]
Complement.not_inc_complement_singleton [in set1]
Complement.strict_sub_nonempty_complement [in set1]
Complement.sub_complement [in set1]
Complement.use_complement [in set1]
Constructions.arrow_EP_exten [in set1]
Constructions.by_cases_if [in set1]
Constructions.by_cases_if_not [in set1]
Constructions.by_cases_nonempty [in set1]
Constructions.B_back [in set1]
Constructions.B_eq [in set1]
Constructions.choosenat_pr [in set1]
Constructions.choose_equiv [in set1]
Constructions.choose_not [in set1]
Constructions.choose_pr [in set1]
Constructions.cut_inc [in set1]
Constructions.cut_pr [in set1]
Constructions.cut_sub [in set1]
Constructions.cut_to_R_eq [in set1]
Constructions.emptyset_dichot [in set1]
Constructions.emptyset_pr [in set1]
Constructions.emptyset_sub_any [in set1]
Constructions.exists_proof [in set1]
Constructions.inc_nonempty [in set1]
Constructions.is_emptyset [in set1]
Constructions.nonemptyT_not_empty [in set1]
Constructions.nonemptyT_not_empty0 [in set1]
Constructions.nonempty_rep [in set1]
Constructions.not_empty_nonemptyT [in set1]
Constructions.not_exists_pr [in set1]
Constructions.R_inc [in set1]
Constructions.strict_sub_trans1 [in set1]
Constructions.strict_sub_trans2 [in set1]
Constructions.sub_refl [in set1]
Constructions.sub_trans [in set1]
Constructions.X_eq [in set1]
Constructions.X_rewrite [in set1]
Constructions.Yt_if_not_rw [in set1]
Constructions.Yt_if_rw [in set1]
Constructions.Yy_if [in set1]
Constructions.Yy_if_not [in set1]
Constructions.Y_if [in set1]
Constructions.Y_if_not [in set1]
Constructions.Y_if_not_rw [in set1]
Constructions.Y_if_rw [in set1]
Constructions.Z_all [in set1]
Constructions.Z_inc [in set1]
Constructions.Z_sub [in set1]
Correspondence.acreate_corresp [in set2]
Correspondence.compose_correspondence [in set2]
Correspondence.compose_domain [in set2]
Correspondence.compose_domain1 [in set2]
Correspondence.compose_identity_identity [in set2]
Correspondence.compose_identity_left [in set2]
Correspondence.compose_identity_right [in set2]
Correspondence.compose_of_sets [in set2]
Correspondence.compose_range [in set2]
Correspondence.compose_range1 [in set2]
Correspondence.compose_related [in set2]
Correspondence.composition_associative [in set2]
Correspondence.composition_increasing [in set2]
Correspondence.composition_is_graph [in set2]
Correspondence.constant_function_p1 [in set2]
Correspondence.corresp_create [in set2]
Correspondence.corresp_graph [in set2]
Correspondence.corresp_is_graph [in set2]
Correspondence.corresp_propb [in set2]
Correspondence.corresp_recov [in set2]
Correspondence.corresp_source [in set2]
Correspondence.corresp_sub_domain [in set2]
Correspondence.corresp_sub_range [in set2]
Correspondence.corresp_target [in set2]
Correspondence.corr_propa [in set2]
Correspondence.corr_propc [in set2]
Correspondence.diagonal_is_identity [in set2]
Correspondence.domain_inverse [in set2]
Correspondence.emptyset_domain [in set2]
Correspondence.emptyset_fgraph [in set2]
Correspondence.emptyset_graph [in set2]
Correspondence.emptyset_range [in set2]
Correspondence.empty_graph1 [in set2]
Correspondence.empty_graph2 [in set2]
Correspondence.identity_corresp [in set2]
Correspondence.identity_graph [in set2]
Correspondence.identity_range [in set2]
Correspondence.identity_self_inverse [in set2]
Correspondence.identity_source [in set2]
Correspondence.identity_target [in set2]
Correspondence.image_by_emptyset [in set2]
Correspondence.image_by_graph_domain [in set2]
Correspondence.image_by_graph_rw [in set2]
Correspondence.image_by_increasing [in set2]
Correspondence.image_by_nonemptyset [in set2]
Correspondence.image_composition [in set2]
Correspondence.image_of_large [in set2]
Correspondence.im_singleton_inclusion [in set2]
Correspondence.im_singleton_pr [in set2]
Correspondence.inc_compose [in set2]
Correspondence.inc_diagonal_rw [in set2]
Correspondence.inc_pair_diagonal [in set2]
Correspondence.inverse_compose [in set2]
Correspondence.inverse_compose_cor [in set2]
Correspondence.inverse_correspondence [in set2]
Correspondence.inverse_direct_image [in set2]
Correspondence.inverse_fun_involutive [in set2]
Correspondence.inverse_graph_alt [in set2]
Correspondence.inverse_graph_emptyset [in set2]
Correspondence.inverse_graph_involutive [in set2]
Correspondence.inverse_graph_is_graph [in set2]
Correspondence.inverse_graph_pair [in set2]
Correspondence.inverse_graph_pr2 [in set2]
Correspondence.inverse_graph_rw [in set2]
Correspondence.inverse_identity_g [in set2]
Correspondence.inverse_product [in set2]
Correspondence.inverse_source [in set2]
Correspondence.inverse_target [in set2]
Correspondence.inv_image_by_fun_pr [in set2]
Correspondence.inv_image_graph_rw [in set2]
Correspondence.is_triple_corr [in set2]
Correspondence.product_domain [in set2]
Correspondence.product_is_graph [in set2]
Correspondence.product_range [in set2]
Correspondence.product_related [in set2]
Correspondence.range_domain_exists [in set2]
Correspondence.range_inverse [in set2]
Correspondence.set_of_correspondences_propa [in set2]
Correspondence.set_of_correspondences_rw [in set2]
Correspondence.sub_emptyset [in set2]
Correspondence.sub_graph_prod [in set2]
Correspondence.sub_image_by_graph [in set2]
F
FiniteSets.bijective_if_same_finite_c_inj [in set8]FiniteSets.bijective_if_same_finite_c_surj [in set8]
FiniteSets.Bnat_interval_cc_pr [in set8]
FiniteSets.Bnat_interval_cc_pr1 [in set8]
FiniteSets.Bnat_interval_co_pr [in set8]
FiniteSets.Bnat_interval_co_pr1 [in set8]
FiniteSets.Bnat_is_cardinal [in set8]
FiniteSets.Bnat_order_le [in set8]
FiniteSets.Bnat_order_substrate [in set8]
FiniteSets.Bnat_order_worder [in set8]
FiniteSets.Bnat_stable_mult [in set8]
FiniteSets.Bnat_stable_plus [in set8]
FiniteSets.Bnat_wordered [in set8]
FiniteSets.cardinal_c_induction [in set8]
FiniteSets.cardinal_c_induction1 [in set8]
FiniteSets.cardinal_c_induction2 [in set8]
FiniteSets.cardinal_c_induction3 [in set8]
FiniteSets.cardinal_c_induction3_v [in set8]
FiniteSets.cardinal_c_induction4 [in set8]
FiniteSets.cardinal_c_induction4_v [in set8]
FiniteSets.cardinal_c_induction_v [in set8]
FiniteSets.cardinal_le_when_complement1 [in set8]
FiniteSets.cardinal_nat_cardinal [in set8]
FiniteSets.cardinal_nat_doubleton [in set8]
FiniteSets.cardinal_nat_emptyset [in set8]
FiniteSets.cardinal_nat_finite_eq [in set8]
FiniteSets.cardinal_nat_finite_eq1 [in set8]
FiniteSets.cardinal_nat_one [in set8]
FiniteSets.cardinal_nat_pr [in set8]
FiniteSets.cardinal_nat_pr1 [in set8]
FiniteSets.cardinal_nat_singleton [in set8]
FiniteSets.cardinal_nat_two [in set8]
FiniteSets.cardinal_nat_zero [in set8]
FiniteSets.cardinal_Rnat_inj [in set8]
FiniteSets.cardinal_Rnat_lt [in set8]
FiniteSets.cardinal_succ [in set8]
FiniteSets.cardinal_succ_pr [in set8]
FiniteSets.cardinal_succ_pr0 [in set8]
FiniteSets.cardinal_succ_pr1 [in set8]
FiniteSets.doubleton_finite [in set8]
FiniteSets.emptyset_finite [in set8]
FiniteSets.exists_nat_cardinal [in set8]
FiniteSets.exists_predc [in set8]
FiniteSets.finite_domain_graph [in set8]
FiniteSets.finite_fun_image [in set8]
FiniteSets.finite_graph_domain [in set8]
FiniteSets.finite_graph_range [in set8]
FiniteSets.finite_image [in set8]
FiniteSets.finite_image_by [in set8]
FiniteSets.finite_in_product [in set8]
FiniteSets.finite_le_infinite [in set8]
FiniteSets.finite_lt_infinite [in set8]
FiniteSets.finite_powerset [in set8]
FiniteSets.finite_range [in set8]
FiniteSets.finite_Rnat [in set8]
FiniteSets.finite_set_induction [in set8]
FiniteSets.finite_set_induction0 [in set8]
FiniteSets.finite_set_induction1 [in set8]
FiniteSets.finite_set_induction2 [in set8]
FiniteSets.finite_set_induction3 [in set8]
FiniteSets.finite_set_maximal [in set8]
FiniteSets.finite_set_torder_greatest [in set8]
FiniteSets.finite_set_torder_worder [in set8]
FiniteSets.finite_subset_directed_bounded [in set8]
FiniteSets.finite_subset_lattice_inf [in set8]
FiniteSets.finite_subset_lattice_sup [in set8]
FiniteSets.finite_subset_torder_greatest [in set8]
FiniteSets.finite_subset_torder_least [in set8]
FiniteSets.finite_union2 [in set8]
FiniteSets.inc0_Bnat [in set8]
FiniteSets.inc1_Bnat [in set8]
FiniteSets.inc2_Bnat [in set8]
FiniteSets.inc_Bnat [in set8]
FiniteSets.inc_Bnat_prop [in set8]
FiniteSets.inc_nat_to_B [in set8]
FiniteSets.inc_pseudo_pseudo [in set8]
FiniteSets.inc_succ_Bnat [in set8]
FiniteSets.integer_is_cardinal [in set8]
FiniteSets.intersection_of_pseudo_ordinals [in set8]
FiniteSets.is_finite0 [in set8]
FiniteSets.is_finite1 [in set8]
FiniteSets.is_finite2 [in set8]
FiniteSets.is_finite3 [in set8]
FiniteSets.is_finite4 [in set8]
FiniteSets.is_finite_in_sum [in set8]
FiniteSets.is_finite_in_sum2 [in set8]
FiniteSets.is_finite_succ [in set8]
FiniteSets.is_finite_succ1 [in set8]
FiniteSets.is_finite_succ2 [in set8]
FiniteSets.is_less_than_succ [in set8]
FiniteSets.is_lt_succ [in set8]
FiniteSets.le_int_in_Bnat [in set8]
FiniteSets.le_int_is_int [in set8]
FiniteSets.lt_is_le_succ [in set8]
FiniteSets.lt_is_le_succ1 [in set8]
FiniteSets.lt_n_succ_le0 [in set8]
FiniteSets.lt_n_succ_le1 [in set8]
FiniteSets.maximal_inclusion [in set8]
FiniteSets.mult_via_plus [in set8]
FiniteSets.nat_B_inj [in set8]
FiniteSets.nat_B_le [in set8]
FiniteSets.nat_B_lt [in set8]
FiniteSets.nat_B_lt0 [in set8]
FiniteSets.nat_B_lt1 [in set8]
FiniteSets.nat_B_mult [in set8]
FiniteSets.nat_B_plus [in set8]
FiniteSets.nat_B_S [in set8]
FiniteSets.nat_B_0 [in set8]
FiniteSets.nat_B_1 [in set8]
FiniteSets.nat_B_2 [in set8]
FiniteSets.nat_infinite_set [in set8]
FiniteSets.nat_to_B_pr [in set8]
FiniteSets.nat_to_B_pr1 [in set8]
FiniteSets.nat_to_B_surjective [in set8]
FiniteSets.of_finite_character_example [in set8]
FiniteSets.plus_via_succ [in set8]
FiniteSets.predc_pr [in set8]
FiniteSets.predc_pr0 [in set8]
FiniteSets.predc_pr1 [in set8]
FiniteSets.predc_pr2 [in set8]
FiniteSets.predc_pr3 [in set8]
FiniteSets.pseudo_not_inc_itself [in set8]
FiniteSets.pseudo_ordinal_dichotomy [in set8]
FiniteSets.pseudo_ordinal_empty [in set8]
FiniteSets.pseudo_ordinal_emptyset [in set8]
FiniteSets.pseudo_ordinal_isomorphism_exists [in set8]
FiniteSets.pseudo_ordinal_isomorphism_unique [in set8]
FiniteSets.pseudo_ordinal_pr [in set8]
FiniteSets.pseudo_ordinal_pr1 [in set8]
FiniteSets.pseudo_ordinal_Rnat [in set8]
FiniteSets.pseudo_ordinal_tack_on [in set8]
FiniteSets.pseudo_ordinal_transitive [in set8]
FiniteSets.pseudo_ordinal_transitive1 [in set8]
FiniteSets.Rnat_inc_lt [in set8]
FiniteSets.Rnat_le_implies_sub [in set8]
FiniteSets.Rnat_lt_implies_inc [in set8]
FiniteSets.Rnat_lt_implies_strict_sub [in set8]
FiniteSets.Rnat_sub_le [in set8]
FiniteSets.Rnot_inc_itself [in set8]
FiniteSets.set_of_finite_subsets_pr [in set8]
FiniteSets.singleton_finite [in set8]
FiniteSets.strict_sub_smaller [in set8]
FiniteSets.strict_sub_smaller1 [in set8]
FiniteSets.sub_finite_set [in set8]
FiniteSets.sub_image_of_fun [in set8]
FiniteSets.succ_cardinal [in set8]
FiniteSets.succ_is_cardinal [in set8]
FiniteSets.succ_nonzero [in set8]
FiniteSets.succ_nonzero1 [in set8]
FiniteSets.succ_positive [in set8]
FiniteSets.succ_zero [in set8]
FiniteSets.S_inj_not_bij [in set8]
FiniteSets.tack_if_succ_card [in set8]
FiniteSets.tack_on_finite [in set8]
FiniteSets.transitive_intersection [in set8]
FiniteSets.transitive_tack_on_itself [in set8]
FiniteSets.transitive_union [in set8]
FiniteSets.value_R_0 [in set8]
FiniteSets.value_R_1 [in set8]
FiniteSets.value_R_2 [in set8]
FiniteSets.value_R_3 [in set8]
FiniteSets.worder_sub_ordinal [in set8]
FiniteSets.zero_lt_one [in set8]
Function.alternate_compose [in set1]
Function.domain_rw [in set1]
Function.domain_union [in set1]
Function.domain_union2 [in set1]
Function.double_restr [in set1]
Function.fcomposable_domain [in set1]
Function.fcompose_domain [in set1]
Function.fcompose_ev [in set1]
Function.fcompose_ev1 [in set1]
Function.fcompose_fgraph [in set1]
Function.fcompose_range [in set1]
Function.fdomain_pr1 [in set1]
Function.fgraph_exten [in set1]
Function.fgraph_is_graph [in set1]
Function.fgraph_pr [in set1]
Function.fgraph_sub [in set1]
Function.fgraph_sub_eq [in set1]
Function.fgraph_sub_V [in set1]
Function.fgraph_union2 [in set1]
Function.frange_inc_rw [in set1]
Function.identity_domain [in set1]
Function.identity_ev [in set1]
Function.identity_fgraph [in set1]
Function.inc_pr1_domain [in set1]
Function.inc_pr2_range [in set1]
Function.inc_V_range [in set1]
Function.inverse_image_inc [in set1]
Function.inverse_image_pr [in set1]
Function.inverse_image_sub [in set1]
Function.in_graph_V [in set1]
Function.is_restriction_pr [in set1]
Function.L_create [in set1]
Function.L_domain [in set1]
Function.L_exten1 [in set1]
Function.L_fgraph [in set1]
Function.L_range [in set1]
Function.L_range_rw [in set1]
Function.L_recovers [in set1]
Function.L_V_out [in set1]
Function.L_V_rewrite [in set1]
Function.pr2_V [in set1]
Function.range_rw [in set1]
Function.range_union [in set1]
Function.range_union2 [in set1]
Function.restr_domain [in set1]
Function.restr_domain1 [in set1]
Function.restr_ev [in set1]
Function.restr_ev1 [in set1]
Function.restr_fgraph [in set1]
Function.restr_graph [in set1]
Function.restr_inc_rw [in set1]
Function.restr_sub [in set1]
Function.restr_to_domain [in set1]
Function.restr_to_domain2 [in set1]
Function.sub_graph_domain [in set1]
Function.sub_graph_ev [in set1]
Function.sub_graph_fgraph [in set1]
Function.sub_graph_range [in set1]
Function.tack_on_domain [in set1]
Function.tack_on_fgraph [in set1]
Function.tack_on_range [in set1]
Function.tcreate_domain [in set1]
Function.tcreate_value_inc [in set1]
Function.tcreate_value_type [in set1]
I
Image.fun_image_rw [in set1]Image.inc_fun_image [in set1]
InfiniteSets.cardinal_comp_singl_inf [in set10]
InfiniteSets.countable_finite_or_N [in set10]
InfiniteSets.countable_finite_or_N_b [in set10]
InfiniteSets.countable_finite_or_N_c [in set10]
InfiniteSets.countable_inv_image [in set10]
InfiniteSets.countable_product [in set10]
InfiniteSets.countable_prop [in set10]
InfiniteSets.countable_subset [in set10]
InfiniteSets.countable_union [in set10]
InfiniteSets.decreasing_prop [in set10]
InfiniteSets.decreasing_stationary [in set10]
InfiniteSets.equipotent_inf2_inf [in set10]
InfiniteSets.equipotent_nat_Bnat [in set10]
InfiniteSets.equipotent_N2_N [in set10]
InfiniteSets.equipotent_range [in set10]
InfiniteSets.finite_family_product [in set10]
InfiniteSets.finite_increasing_stationary [in set10]
InfiniteSets.increasing_prop [in set10]
InfiniteSets.increasing_stationary [in set10]
InfiniteSets.induction_defined_pr [in set10]
InfiniteSets.induction_defined_pr0 [in set10]
InfiniteSets.induction_defined_pr1 [in set10]
InfiniteSets.induction_defined_pr_set [in set10]
InfiniteSets.induction_defined_pr_set0 [in set10]
InfiniteSets.induction_defined_pr_set1 [in set10]
InfiniteSets.infinite_Bnat [in set10]
InfiniteSets.infinite_finite_sequence [in set10]
InfiniteSets.infinite_finite_subsets [in set10]
InfiniteSets.infinite_greater_countable [in set10]
InfiniteSets.infinite_greater_countable1 [in set10]
InfiniteSets.infinite_partition [in set10]
InfiniteSets.integer_induction [in set10]
InfiniteSets.integer_induction0 [in set10]
InfiniteSets.integer_induction1 [in set10]
InfiniteSets.integer_induction_stable [in set10]
InfiniteSets.integer_induction_stable0 [in set10]
InfiniteSets.integer_induction_stable1 [in set10]
InfiniteSets.morphism_range [in set10]
InfiniteSets.morphism_range1 [in set10]
InfiniteSets.noetherian_induction [in set10]
InfiniteSets.notbig_family_sum [in set10]
InfiniteSets.notbig_family_sum1 [in set10]
InfiniteSets.power_of_infinite [in set10]
InfiniteSets.product2_infinite [in set10]
InfiniteSets.segment_Bnat_order [in set10]
InfiniteSets.sum2_infinite [in set10]
IntegerProps.app_nth3 [in set9]
IntegerProps.back_to_nat_pr [in set9]
IntegerProps.back_to_nat_pr1 [in set9]
IntegerProps.back_to_nat_pr2 [in set9]
IntegerProps.bijective_complement [in set9]
IntegerProps.binomial1 [in set9]
IntegerProps.binomial2 [in set9]
IntegerProps.binomial3 [in set9]
IntegerProps.binomial4 [in set9]
IntegerProps.binomial5 [in set9]
IntegerProps.binomial7 [in set9]
IntegerProps.binom0 [in set9]
IntegerProps.binom1 [in set9]
IntegerProps.binom2 [in set9]
IntegerProps.binom2a [in set9]
IntegerProps.binom_alt_pr [in set9]
IntegerProps.binom_monotone1 [in set9]
IntegerProps.binom_monotone2 [in set9]
IntegerProps.binom_nn [in set9]
IntegerProps.binom_pr [in set9]
IntegerProps.binom_pr0 [in set9]
IntegerProps.binom_pr1 [in set9]
IntegerProps.binom_pr2 [in set9]
IntegerProps.binom_pr3 [in set9]
IntegerProps.binom_symmetric [in set9]
IntegerProps.binom_2plus [in set9]
IntegerProps.binom_2plus0 [in set9]
IntegerProps.Bnat_division [in set9]
IntegerProps.Bnat_infinite [in set9]
IntegerProps.Bnat_le_antisymmetric [in set9]
IntegerProps.Bnat_le_reflexive [in set9]
IntegerProps.Bnat_le_transitive [in set9]
IntegerProps.Bnat_mult_le_simplifiable [in set9]
IntegerProps.Bnat_mult_lt_simplifiable [in set9]
IntegerProps.Bnat_plus_le_simplifiable [in set9]
IntegerProps.Bnat_plus_lt_simplifiable [in set9]
IntegerProps.Bnat_stable_pow [in set9]
IntegerProps.Bnat_stable_sub [in set9]
IntegerProps.Bnat_total_order [in set9]
IntegerProps.Bnat_zero_smallest [in set9]
IntegerProps.Bnat_zero_smallest1 [in set9]
IntegerProps.b_power_k_large [in set9]
IntegerProps.cardinal_complement [in set9]
IntegerProps.cardinal_complement1 [in set9]
IntegerProps.cardinal_complement_image [in set9]
IntegerProps.cardinal_c_induction5_v [in set9]
IntegerProps.cardinal_interval [in set9]
IntegerProps.cardinal_interval0a [in set9]
IntegerProps.cardinal_interval1a [in set9]
IntegerProps.cardinal_interval_co_0a [in set9]
IntegerProps.cardinal_interval_co_0a1 [in set9]
IntegerProps.cardinal_le_a_apowb [in set9]
IntegerProps.cardinal_lt_pr [in set9]
IntegerProps.cardinal_pairs_le [in set9]
IntegerProps.cardinal_pairs_lt [in set9]
IntegerProps.cardinal_set_of_increasing_functions [in set9]
IntegerProps.cardinal_set_of_increasing_functions1 [in set9]
IntegerProps.cardinal_set_of_increasing_functions2 [in set9]
IntegerProps.cardinal_set_of_increasing_functions3 [in set9]
IntegerProps.cardinal_set_of_increasing_functions4 [in set9]
IntegerProps.card_interval_c0_pr [in set9]
IntegerProps.card_set_of_increasing_functions_int [in set9]
IntegerProps.card_sub_associative [in set9]
IntegerProps.card_sub_associativeN [in set9]
IntegerProps.card_sub_associative1 [in set9]
IntegerProps.card_sub_associative1N [in set9]
IntegerProps.card_sub_non_zero [in set9]
IntegerProps.card_sub_pr [in set9]
IntegerProps.card_sub_pr0 [in set9]
IntegerProps.card_sub_pr1 [in set9]
IntegerProps.card_sub_pr2 [in set9]
IntegerProps.card_sub_pr4 [in set9]
IntegerProps.card_sub_pr4N [in set9]
IntegerProps.card_sub_wrong [in set9]
IntegerProps.chart_fun_injective [in set9]
IntegerProps.char_fun_axioms [in set9]
IntegerProps.char_fun_complement [in set9]
IntegerProps.char_fun_constant [in set9]
IntegerProps.char_fun_function [in set9]
IntegerProps.char_fun_inter [in set9]
IntegerProps.char_fun_union [in set9]
IntegerProps.char_fun_W [in set9]
IntegerProps.char_fun_W_a [in set9]
IntegerProps.char_fun_W_aa [in set9]
IntegerProps.char_fun_W_b [in set9]
IntegerProps.char_fun_W_bb [in set9]
IntegerProps.char_fun_W_cardinal [in set9]
IntegerProps.contraction_assoc [in set9]
IntegerProps.distrib_prod2_sub [in set9]
IntegerProps.distrib_prod2_subN [in set9]
IntegerProps.divides_and_difference [in set9]
IntegerProps.divides_and_sum [in set9]
IntegerProps.division_exists [in set9]
IntegerProps.division_prop_alt [in set9]
IntegerProps.division_prop_nat [in set9]
IntegerProps.division_result_integer [in set9]
IntegerProps.division_unique [in set9]
IntegerProps.domain_restr_empty [in set9]
IntegerProps.double_compl_ex [in set9]
IntegerProps.double_compl_nat [in set9]
IntegerProps.double_restrc [in set9]
IntegerProps.double_sub [in set9]
IntegerProps.double_subN [in set9]
IntegerProps.emptyset_interval_00 [in set9]
IntegerProps.equipotent_restriction [in set9]
IntegerProps.factorial0 [in set9]
IntegerProps.factorial1 [in set9]
IntegerProps.factorial2 [in set9]
IntegerProps.factorial_nonzero [in set9]
IntegerProps.factorial_prop [in set9]
IntegerProps.factorial_prop1 [in set9]
IntegerProps.factorial_succ [in set9]
IntegerProps.fct_prod0 [in set9]
IntegerProps.fct_prod_const [in set9]
IntegerProps.fct_prod_mult [in set9]
IntegerProps.fct_prod_rec [in set9]
IntegerProps.fct_prod_rec1 [in set9]
IntegerProps.fct_prod_rev [in set9]
IntegerProps.fct_sum0 [in set9]
IntegerProps.fct_sum_const [in set9]
IntegerProps.fct_sum_const1 [in set9]
IntegerProps.fct_sum_plus [in set9]
IntegerProps.fct_sum_rec [in set9]
IntegerProps.fct_sum_rec1 [in set9]
IntegerProps.fct_sum_rev [in set9]
IntegerProps.fct_to_listB_pr0 [in set9]
IntegerProps.fct_to_listB_pr1 [in set9]
IntegerProps.fct_to_listB_pr2 [in set9]
IntegerProps.fct_to_listB_pr3 [in set9]
IntegerProps.fct_to_list_length [in set9]
IntegerProps.fct_to_list_lengthB [in set9]
IntegerProps.fct_to_list_unique [in set9]
IntegerProps.fct_to_rev [in set9]
IntegerProps.finite_c_set [in set9]
IntegerProps.finite_lt_a_ab [in set9]
IntegerProps.finite_ordered_interval [in set9]
IntegerProps.finite_ordered_interval1 [in set9]
IntegerProps.finite_powerset [in set9]
IntegerProps.finite_power_lt1 [in set9]
IntegerProps.finite_power_lt1N [in set9]
IntegerProps.finite_power_lt2 [in set9]
IntegerProps.finite_power_lt2N [in set9]
IntegerProps.finite_product_finite [in set9]
IntegerProps.finite_product_finite_aux [in set9]
IntegerProps.finite_product_finite_set [in set9]
IntegerProps.finite_product_lt [in set9]
IntegerProps.finite_prod2_lt [in set9]
IntegerProps.finite_set_interval_Bnat [in set9]
IntegerProps.finite_set_interval_co [in set9]
IntegerProps.finite_sum2_lt [in set9]
IntegerProps.finite_sum3_lt [in set9]
IntegerProps.finite_sum_finite [in set9]
IntegerProps.finite_sum_finite_aux [in set9]
IntegerProps.finite_sum_lt [in set9]
IntegerProps.finite_union_finite [in set9]
IntegerProps.function_on_nat_pr [in set9]
IntegerProps.function_on_nat_pr1 [in set9]
IntegerProps.increasing_compose [in set9]
IntegerProps.increasing_compose3 [in set9]
IntegerProps.increasing_prop [in set9]
IntegerProps.increasing_prop1 [in set9]
IntegerProps.inc_a_interval_co_succ [in set9]
IntegerProps.inc_function_on_nat_Bnat [in set9]
IntegerProps.inc_quotient_bnat [in set9]
IntegerProps.inc_remainder_bnat [in set9]
IntegerProps.induction_on_prod [in set9]
IntegerProps.induction_on_prod0 [in set9]
IntegerProps.induction_on_prod1 [in set9]
IntegerProps.induction_on_prod2 [in set9]
IntegerProps.induction_on_prod4 [in set9]
IntegerProps.induction_on_prod5 [in set9]
IntegerProps.induction_on_sum [in set9]
IntegerProps.induction_on_sum0 [in set9]
IntegerProps.induction_on_sum1 [in set9]
IntegerProps.induction_on_sum2 [in set9]
IntegerProps.induction_on_sum3 [in set9]
IntegerProps.induction_on_sum4 [in set9]
IntegerProps.induction_on_sum5 [in set9]
IntegerProps.interval_Bnatco_related [in set9]
IntegerProps.interval_Bnatco_substrate [in set9]
IntegerProps.interval_Bnatco_worder [in set9]
IntegerProps.interval_Bnato_related [in set9]
IntegerProps.interval_Bnato_related1 [in set9]
IntegerProps.interval_Bnato_related2 [in set9]
IntegerProps.interval_Bnato_substrate [in set9]
IntegerProps.interval_Bnato_worder [in set9]
IntegerProps.interval_Bnat_pr [in set9]
IntegerProps.interval_Bnat_pr0 [in set9]
IntegerProps.interval_cc_0a_increasing [in set9]
IntegerProps.interval_cc_0a_increasing1 [in set9]
IntegerProps.interval_co_cc [in set9]
IntegerProps.interval_co_pr4 [in set9]
IntegerProps.interval_co_0a_increasing [in set9]
IntegerProps.interval_co_0a_increasing1 [in set9]
IntegerProps.interval_co_0a_pr [in set9]
IntegerProps.interval_co_0a_pr1 [in set9]
IntegerProps.interval_co_0a_pr2 [in set9]
IntegerProps.interval_co_0a_pr3 [in set9]
IntegerProps.interval_co_0a_restr [in set9]
IntegerProps.isomorphism_worder_finite [in set9]
IntegerProps.is_expansion_exists [in set9]
IntegerProps.is_expansion_exists1 [in set9]
IntegerProps.is_expansion_prop0 [in set9]
IntegerProps.is_expansion_prop1 [in set9]
IntegerProps.is_expansion_prop10 [in set9]
IntegerProps.is_expansion_prop11 [in set9]
IntegerProps.is_expansion_prop2 [in set9]
IntegerProps.is_expansion_prop3 [in set9]
IntegerProps.is_expansion_prop4 [in set9]
IntegerProps.is_expansion_prop5 [in set9]
IntegerProps.is_expansion_prop6 [in set9]
IntegerProps.is_expansion_prop7 [in set9]
IntegerProps.is_expansion_prop8 [in set9]
IntegerProps.is_expansion_prop9 [in set9]
IntegerProps.is_expansion_unique [in set9]
IntegerProps.is_finite_in_product [in set9]
IntegerProps.least_int_prop [in set9]
IntegerProps.least_int_prop0 [in set9]
IntegerProps.least_int_prop1 [in set9]
IntegerProps.length_app1 [in set9]
IntegerProps.length_app2 [in set9]
IntegerProps.le_one_not_zero [in set9]
IntegerProps.list_extens [in set9]
IntegerProps.list_prod_app [in set9]
IntegerProps.list_prod_cons [in set9]
IntegerProps.list_prod_consr [in set9]
IntegerProps.list_prod_pr [in set9]
IntegerProps.list_prod_rev [in set9]
IntegerProps.list_prod_single [in set9]
IntegerProps.list_prop1 [in set9]
IntegerProps.list_prop2 [in set9]
IntegerProps.list_prop3 [in set9]
IntegerProps.list_prop_app [in set9]
IntegerProps.list_prop_nth [in set9]
IntegerProps.list_prop_refine [in set9]
IntegerProps.list_range_pr [in set9]
IntegerProps.list_range_pr1 [in set9]
IntegerProps.list_subset_cons [in set9]
IntegerProps.list_sum_app [in set9]
IntegerProps.list_sum_cons [in set9]
IntegerProps.list_sum_consr [in set9]
IntegerProps.list_sum_pr [in set9]
IntegerProps.list_sum_rev [in set9]
IntegerProps.list_sum_single [in set9]
IntegerProps.list_to_fB_axioms [in set9]
IntegerProps.list_to_fB_function [in set9]
IntegerProps.list_to_fB_pr [in set9]
IntegerProps.list_to_fB_W [in set9]
IntegerProps.list_to_fB_W1 [in set9]
IntegerProps.list_to_fct_pr [in set9]
IntegerProps.list_to_fct_pr0 [in set9]
IntegerProps.list_to_fct_pr0B [in set9]
IntegerProps.list_to_fct_pr1 [in set9]
IntegerProps.list_to_fct_pr1B [in set9]
IntegerProps.list_to_fct_pr3 [in set9]
IntegerProps.list_to_fct_pr3B [in set9]
IntegerProps.list_to_fct_pr4 [in set9]
IntegerProps.list_to_fct_pr4B [in set9]
IntegerProps.list_to_f_axioms [in set9]
IntegerProps.list_to_f_consB0 [in set9]
IntegerProps.list_to_f_consB1 [in set9]
IntegerProps.list_to_f_consB2 [in set9]
IntegerProps.list_to_f_consB3 [in set9]
IntegerProps.list_to_f_cons0 [in set9]
IntegerProps.list_to_f_cons1 [in set9]
IntegerProps.list_to_f_cons2 [in set9]
IntegerProps.list_to_f_cons3 [in set9]
IntegerProps.list_to_f_function [in set9]
IntegerProps.list_to_f_pr1 [in set9]
IntegerProps.list_to_f_pr2 [in set9]
IntegerProps.list_to_f_W [in set9]
IntegerProps.list_to_f_W1 [in set9]
IntegerProps.list_to_f_W2 [in set9]
IntegerProps.lt_a_power_b_a [in set9]
IntegerProps.lt_a_power_b_aN [in set9]
IntegerProps.lt_i_n [in set9]
IntegerProps.lt_n_succ_le [in set9]
IntegerProps.lt_n_succ_leN [in set9]
IntegerProps.lt_plus [in set9]
IntegerProps.lt_to_plus [in set9]
IntegerProps.l_to_fct [in set9]
IntegerProps.l_to_fct1 [in set9]
IntegerProps.l_to_fct2 [in set9]
IntegerProps.minus_n_nC [in set9]
IntegerProps.minus_n_0C [in set9]
IntegerProps.minus_SnSi [in set9]
IntegerProps.minus_wrong [in set9]
IntegerProps.mult_le_lt_compat [in set9]
IntegerProps.mult_lt_le_compat [in set9]
IntegerProps.mult_lt_reg_l [in set9]
IntegerProps.mult_lt_reg_r [in set9]
IntegerProps.mult_simplifiable_left [in set9]
IntegerProps.mult_simplifiable_leftN [in set9]
IntegerProps.mult_simplifiable_right [in set9]
IntegerProps.mult_simplifiable_rightN [in set9]
IntegerProps.mult_S_lt_reg_l [in set9]
IntegerProps.mutually_disjoint_prop1 [in set9]
IntegerProps.nat_B_division [in set9]
IntegerProps.nat_B_pow [in set9]
IntegerProps.nat_B_pred [in set9]
IntegerProps.nat_B_quo [in set9]
IntegerProps.nat_B_rem [in set9]
IntegerProps.nat_B_sub [in set9]
IntegerProps.nat_not_zero_pr [in set9]
IntegerProps.Ndivides_itself [in set9]
IntegerProps.Ndivides_pr [in set9]
IntegerProps.Ndivides_pr1 [in set9]
IntegerProps.Ndivides_pr2 [in set9]
IntegerProps.Ndivides_pr3 [in set9]
IntegerProps.Ndivides_pr4 [in set9]
IntegerProps.Ndivides_trans [in set9]
IntegerProps.Ndivides_trans1 [in set9]
IntegerProps.Ndivides_trans2 [in set9]
IntegerProps.Ndivision_existence [in set9]
IntegerProps.Ndivision_exists [in set9]
IntegerProps.Ndivision_itself [in set9]
IntegerProps.Ndivision_of_zero [in set9]
IntegerProps.Ndivision_pr [in set9]
IntegerProps.Ndivision_pr_q [in set9]
IntegerProps.Ndivision_pr_r [in set9]
IntegerProps.Ndivision_unique [in set9]
IntegerProps.nonzero_suc [in set9]
IntegerProps.non_zero_apowb [in set9]
IntegerProps.non_zero_apowbN [in set9]
IntegerProps.non_zero_mult [in set9]
IntegerProps.Nquo_itself [in set9]
IntegerProps.Nquo_simplify [in set9]
IntegerProps.number_of_injections_base [in set9]
IntegerProps.number_of_injections_pr [in set9]
IntegerProps.number_of_injections_prop [in set9]
IntegerProps.number_of_injections_rec [in set9]
IntegerProps.number_of_partitions [in set9]
IntegerProps.number_of_partitions1 [in set9]
IntegerProps.number_of_partitions2 [in set9]
IntegerProps.number_of_partitions3 [in set9]
IntegerProps.number_of_partitions4 [in set9]
IntegerProps.number_of_partitions5 [in set9]
IntegerProps.number_of_partitions6 [in set9]
IntegerProps.number_of_partitions7 [in set9]
IntegerProps.number_of_partitions_bis [in set9]
IntegerProps.number_of_permutations [in set9]
IntegerProps.one_divides_all [in set9]
IntegerProps.partition_complement [in set9]
IntegerProps.partition_tack_on [in set9]
IntegerProps.partition_tack_on_intco [in set9]
IntegerProps.plus_minusC [in set9]
IntegerProps.plus_n_Sm_subSm [in set9]
IntegerProps.plus_n_Sm_subSn [in set9]
IntegerProps.plus_reg_r [in set9]
IntegerProps.plus_simplifiable_left [in set9]
IntegerProps.plus_simplifiable_leftN [in set9]
IntegerProps.plus_simplifiable_right [in set9]
IntegerProps.plus_simplifiable_rightN [in set9]
IntegerProps.power_of_prodN [in set9]
IntegerProps.power_of_sumN [in set9]
IntegerProps.power_x_0N [in set9]
IntegerProps.power_x_1N [in set9]
IntegerProps.power_0_x [in set9]
IntegerProps.power_0_0N [in set9]
IntegerProps.power_1_xN [in set9]
IntegerProps.power_2_4 [in set9]
IntegerProps.pow_succ [in set9]
IntegerProps.prec_pr1 [in set9]
IntegerProps.pred_minus [in set9]
IntegerProps.prod_increasing6 [in set9]
IntegerProps.quotient_by_one [in set9]
IntegerProps.quotient_of_factorials [in set9]
IntegerProps.quotient_of_factorials1 [in set9]
IntegerProps.restr_plus_interval_isomorphism [in set9]
IntegerProps.restr_plus_minus_bij [in set9]
IntegerProps.rest_minus_interval_axioms [in set9]
IntegerProps.rest_plus_interval_axioms [in set9]
IntegerProps.set_of_functions_sum0 [in set9]
IntegerProps.set_of_functions_sum1 [in set9]
IntegerProps.set_of_functions_sum2 [in set9]
IntegerProps.set_of_functions_sum3 [in set9]
IntegerProps.set_of_functions_sum4 [in set9]
IntegerProps.set_of_functions_sum_pr [in set9]
IntegerProps.shepherd_principle [in set9]
IntegerProps.Sn_is_plus1 [in set9]
IntegerProps.Sn_is_1plus [in set9]
IntegerProps.special_cardinal_positive [in set9]
IntegerProps.strict_increasing_prop [in set9]
IntegerProps.strict_increasing_prop1 [in set9]
IntegerProps.strict_increasing_prop2 [in set9]
IntegerProps.strict_increasing_prop3 [in set9]
IntegerProps.subsets_with_p_elements_pr [in set9]
IntegerProps.sub_increasing2 [in set9]
IntegerProps.sub_interval_Bnat [in set9]
IntegerProps.sub_interval_co_0a_Bnat [in set9]
IntegerProps.sub_le_symmetry [in set9]
IntegerProps.sub_lt_symmetry [in set9]
IntegerProps.sum_increasing4 [in set9]
IntegerProps.sum_increasing5 [in set9]
IntegerProps.sum_increasing6 [in set9]
IntegerProps.sum_of_binomial [in set9]
IntegerProps.sum_of_binomial1 [in set9]
IntegerProps.sum_of_binomial2 [in set9]
IntegerProps.sum_of_i [in set9]
IntegerProps.sum_of_i2 [in set9]
IntegerProps.sum_of_i3 [in set9]
IntegerProps.sum_to_increasing1 [in set9]
IntegerProps.sum_to_increasing2 [in set9]
IntegerProps.sum_to_increasing4 [in set9]
IntegerProps.sum_to_increasing5 [in set9]
IntegerProps.sum_to_increasing6 [in set9]
IntegerProps.tack_on_nat [in set9]
IntegerProps.trivial_cardinal_prod3 [in set9]
IntegerProps.trivial_cardinal_sum3 [in set9]
IntegerProps.two_plus_two [in set9]
IntegerProps.two_times_n [in set9]
IntegerProps.two_times_two [in set9]
IntegerProps.zero_lt_oneN [in set9]
Intersection.intersection2comm [in set1]
Intersection.intersection2idem [in set1]
Intersection.intersection2sub_first [in set1]
Intersection.intersection2sub_second [in set1]
Intersection.intersection2_both [in set1]
Intersection.intersection2_first [in set1]
Intersection.intersection2_inc [in set1]
Intersection.intersection2_second [in set1]
Intersection.intersection2_sub [in set1]
Intersection.intersection_forall [in set1]
Intersection.intersection_inc [in set1]
Intersection.intersection_sub [in set1]
L
Little.doubleton_first [in set1]Little.doubleton_inj [in set1]
Little.doubleton_or [in set1]
Little.doubleton_rw [in set1]
Little.doubleton_second [in set1]
Little.doubleton_singleton [in set1]
Little.doubleton_symm [in set1]
Little.inc_TPa_two_points [in set1]
Little.inc_TPb_two_points [in set1]
Little.nonempty_doubleton [in set1]
Little.nonempty_singleton [in set1]
Little.singleton_eq [in set1]
Little.singleton_inc [in set1]
Little.singleton_inj [in set1]
Little.singleton_rw [in set1]
Little.sub_doubleton [in set1]
Little.sub_singleton [in set1]
Little.two_points_distinct [in set1]
Little.two_points_distinctb [in set1]
Little.two_points_pr [in set1]
Little.two_points_pr2 [in set1]
O
Ordinals.canonical2_substrate [in set11]Ordinals.canonical_du2_pr [in set11]
Ordinals.canonical_du2_rw [in set11]
Ordinals.du_index_pr [in set11]
Ordinals.du_index_pr1 [in set11]
Ordinals.emptyset_order [in set11]
Ordinals.emptyset_substrate [in set11]
Ordinals.inc_disjoint_union [in set11]
Ordinals.inc_disjoint_union1 [in set11]
Ordinals.is_ordinal_omega [in set11]
Ordinals.is_ordinal_0 [in set11]
Ordinals.is_ordinal_1 [in set11]
Ordinals.is_ordinal_2 [in set11]
Ordinals.lexorder_gle1 [in set11]
Ordinals.lexorder_worder [in set11]
Ordinals.order_isomorphic_reflexive [in set11]
Ordinals.order_isomorphic_symmetric [in set11]
Ordinals.order_isomorphic_transitive [in set11]
Ordinals.order_isomorphism_pr [in set11]
Ordinals.order_isomorphism_pr1 [in set11]
Ordinals.order_isomorphism_pr2 [in set11]
Ordinals.order_prod_invariant4 [in set11]
Ordinals.order_sum_invariant4 [in set11]
Ordinals.order_type_le_preorder [in set11]
Ordinals.ordinal0_pr [in set11]
Ordinals.ordinal0_pr1 [in set11]
Ordinals.ordinal_product2_gle [in set11]
Ordinals.ordinal_product2_order [in set11]
Ordinals.ordinal_product2_substrate [in set11]
Ordinals.ordinal_product2_worder [in set11]
Ordinals.ordinal_product_pr [in set11]
Ordinals.ordinal_product_pr1 [in set11]
Ordinals.ordinal_product_pr2 [in set11]
Ordinals.ordinal_product_pr3 [in set11]
Ordinals.ordinal_product_pr4 [in set11]
Ordinals.ordinal_prod2_axioms [in set11]
Ordinals.ordinal_pr1 [in set11]
Ordinals.ordinal_pr10 [in set11]
Ordinals.ordinal_pr2 [in set11]
Ordinals.ordinal_pr3 [in set11]
Ordinals.ordinal_pr4 [in set11]
Ordinals.ordinal_pr5 [in set11]
Ordinals.ordinal_pr6 [in set11]
Ordinals.ordinal_pr7 [in set11]
Ordinals.ordinal_pr8 [in set11]
Ordinals.ordinal_pr9 [in set11]
Ordinals.ordinal_sum2_axioms [in set11]
Ordinals.ordinal_sum2_gle [in set11]
Ordinals.ordinal_sum2_gle_spec [in set11]
Ordinals.ordinal_sum2_order [in set11]
Ordinals.ordinal_sum2_substrate [in set11]
Ordinals.ordinal_sum2_totalorder [in set11]
Ordinals.ordinal_sum2_worder [in set11]
Ordinals.ordinal_sum_assoc1 [in set11]
Ordinals.ordinal_sum_assoc_aux1 [in set11]
Ordinals.ordinal_sum_assoc_aux2 [in set11]
Ordinals.ordinal_sum_assoc_aux3 [in set11]
Ordinals.ordinal_sum_assoc_iso [in set11]
Ordinals.ordinal_sum_distributive [in set11]
Ordinals.ordinal_sum_order [in set11]
Ordinals.ordinal_sum_related [in set11]
Ordinals.ordinal_sum_related1 [in set11]
Ordinals.ordinal_sum_related_id [in set11]
Ordinals.ordinal_sum_substrate [in set11]
Ordinals.ordinal_sum_totalorder [in set11]
Ordinals.ordinal_sum_worder [in set11]
Ordinals.ordinal_1_indep [in set11]
Ordinals.ordinal_1_value [in set11]
Ordinals.ordinal_1_value_bis [in set11]
Ordinals.ord_prod2_ordinal [in set11]
Ordinals.ord_prod2_pr [in set11]
Ordinals.ord_prod2_type [in set11]
Ordinals.ord_prod_emptyset [in set11]
Ordinals.ord_prod_invariant1 [in set11]
Ordinals.ord_prod_invariant2 [in set11]
Ordinals.ord_prod_invariant3 [in set11]
Ordinals.ord_prod_ordinal [in set11]
Ordinals.ord_prod_singleton [in set11]
Ordinals.ord_prod_type [in set11]
Ordinals.ord_sum2_ordinal [in set11]
Ordinals.ord_sum2_pr [in set11]
Ordinals.ord_sum2_type [in set11]
Ordinals.ord_sum_emptyset [in set11]
Ordinals.ord_sum_invariant1 [in set11]
Ordinals.ord_sum_invariant2 [in set11]
Ordinals.ord_sum_invariant3 [in set11]
Ordinals.ord_sum_ordinal [in set11]
Ordinals.ord_sum_singleton [in set11]
Ordinals.ord_sum_type [in set11]
Ordinals.ord_0_plus_unit_l [in set11]
Ordinals.ord_0_plus_unit_r [in set11]
Ordinals.ord_0_prod_l [in set11]
Ordinals.ord_0_prod_r [in set11]
Ordinals.ord_1_mult_unit_l [in set11]
Ordinals.ord_1_mult_unit_r [in set11]
Ordinals.prod_of_substrates_pr [in set11]
Ordinals.singleton_order_isomorphic [in set11]
Ordinals.singleton_order_isomorphic1 [in set11]
Ordinals.singleton_order_isomorphic2 [in set11]
Ordinals.singleton_worder [in set11]
Ordinals.worder_invariance [in set11]
P
Pair.is_pair_rw [in set1]Pair.kpair_recov [in set1]
Pair.kpr0_pair [in set1]
Pair.kpr1_def [in set1]
Pair.kpr1_pair [in set1]
Pair.kpr2_def [in set1]
Pair.kpr2_pair [in set1]
Pair.pair_distinct [in set1]
Pair.pair_distincta [in set1]
Pair.pair_extensionality [in set1]
Pair.pair_is_kpair [in set1]
Pair.pair_is_pair [in set1]
Pair.pair_recov [in set1]
Pair.pr1_def [in set1]
Pair.pr1_injective_x [in set1]
Pair.pr1_pair [in set1]
Pair.pr2_def [in set1]
Pair.pr2_injective_x [in set1]
Pair.pr2_pair [in set1]
Pair.V_inc [in set1]
Pair.V_or [in set1]
Powerset.inc_x_powerset_x [in set1]
Powerset.powerset_inc [in set1]
Powerset.powerset_inc_rw [in set1]
Powerset.powerset_sub [in set1]
R
Relation.canonical_decomposition [in set4]Relation.canonical_decompositiona [in set4]
Relation.canonical_decompositionb [in set4]
Relation.canonical_decomposition_surj [in set4]
Relation.canonical_decomposition_surj2 [in set4]
Relation.canonical_foq_induced_rel_bijective [in set4]
Relation.canon_proj_diagonal_bijective [in set4]
Relation.canon_proj_function [in set4]
Relation.canon_proj_inc [in set4]
Relation.canon_proj_show_surjective [in set4]
Relation.canon_proj_source [in set4]
Relation.canon_proj_surjective [in set4]
Relation.canon_proj_target [in set4]
Relation.canon_proj_W [in set4]
Relation.class_dichot [in set4]
Relation.class_is_cut [in set4]
Relation.class_is_inv_direct_value [in set4]
Relation.class_prod_of_rel2 [in set4]
Relation.class_rep [in set4]
Relation.coarsest_equivalence [in set4]
Relation.coarse_equivalence [in set4]
Relation.coarse_graph [in set4]
Relation.coarse_related [in set4]
Relation.coarse_substrate [in set4]
Relation.compatible_constant_on_classes [in set4]
Relation.compatible_constant_on_classes2 [in set4]
Relation.compatible_ea [in set4]
Relation.compatible_ext_to_prod [in set4]
Relation.compatible_ext_to_prod_inv [in set4]
Relation.compatible_injection_induced_rel [in set4]
Relation.compatible_with_equiv_pr [in set4]
Relation.compatible_with_finer [in set4]
Relation.compatible_with_pr [in set4]
Relation.compatible_with_proj [in set4]
Relation.compatible_with_proj3 [in set4]
Relation.compatible_with_pr2 [in set4]
Relation.composable_fun_proj [in set4]
Relation.composable_fun_projc [in set4]
Relation.composable_fun_projcs [in set4]
Relation.composable_fun_projs [in set4]
Relation.compose_foq_proj [in set4]
Relation.compose_fun_proj_eq [in set4]
Relation.compose_fun_proj_eq2 [in set4]
Relation.compose_fun_proj_ev [in set4]
Relation.compose_fun_proj_ev2 [in set4]
Relation.cqr_aux [in set4]
Relation.decomposable_ext_to_prod_rel [in set4]
Relation.diagonal_class [in set4]
Relation.diagonal_equivalence [in set4]
Relation.diagonal_equivalence1 [in set4]
Relation.diagonal_equivalence2 [in set4]
Relation.diagonal_substrate [in set4]
Relation.domain_is_substrate [in set4]
Relation.ea_equivalence [in set4]
Relation.ea_foq_injective [in set4]
Relation.ea_foq_on_im_bijective [in set4]
Relation.ea_related [in set4]
Relation.equipotent_equivalence [in set4]
Relation.equivalence_equivalence [in set4]
Relation.equivalence_has_graph [in set4]
Relation.equivalence_has_graph0 [in set4]
Relation.equivalence_has_graph2 [in set4]
Relation.equivalence_if_has_graph [in set4]
Relation.equivalence_if_has_graph2 [in set4]
Relation.equivalence_is_graph [in set4]
Relation.equivalence_pr [in set4]
Relation.equivalence_prod_of_rel [in set4]
Relation.equivalence_relation_bourbaki_ex5 [in set4]
Relation.equivalence_relation_pr1 [in set4]
Relation.exists_fun_on_quotient [in set4]
Relation.exists_unique_fun_on_quotient [in set4]
Relation.ext_to_prod_rel_function [in set4]
Relation.ext_to_prod_rel_W [in set4]
Relation.finer_sub_equiv [in set4]
Relation.finer_sub_equiv2 [in set4]
Relation.finer_sub_equiv3 [in set4]
Relation.finest_equivalence [in set4]
Relation.first_proj_class [in set4]
Relation.first_proj_equivalence [in set4]
Relation.first_proj_equiv_proj [in set4]
Relation.first_proj_eq_pr [in set4]
Relation.first_proj_eq_related [in set4]
Relation.first_proj_graph [in set4]
Relation.first_proj_substrate [in set4]
Relation.foqcs_axioms [in set4]
Relation.foqcs_function [in set4]
Relation.foqcs_W [in set4]
Relation.foqc_axioms [in set4]
Relation.foqc_function [in set4]
Relation.foqc_W [in set4]
Relation.foqs_axioms [in set4]
Relation.foqs_function [in set4]
Relation.foqs_W [in set4]
Relation.foq_axioms [in set4]
Relation.foq_finer_function [in set4]
Relation.foq_finer_surjective [in set4]
Relation.foq_finer_W [in set4]
Relation.foq_function [in set4]
Relation.foq_induced_rel_image [in set4]
Relation.foq_induced_rel_injective [in set4]
Relation.foq_W [in set4]
Relation.fun_on_quotient_pr [in set4]
Relation.fun_on_quotient_pr2 [in set4]
Relation.fun_on_quotient_pr3 [in set4]
Relation.fun_on_quotient_pr4 [in set4]
Relation.fun_on_quotient_pr5 [in set4]
Relation.graph_ea_equivalence [in set4]
Relation.graph_ea_substrate [in set4]
Relation.graph_of_ea [in set4]
Relation.graph_on_graph [in set4]
Relation.graph_on_rw0 [in set4]
Relation.graph_on_rw1 [in set4]
Relation.graph_on_rw2 [in set4]
Relation.graph_on_substrate [in set4]
Relation.idempotent_graph_transitive [in set4]
Relation.iirel_class [in set4]
Relation.iirel_function [in set4]
Relation.iirel_related [in set4]
Relation.iirel_relation [in set4]
Relation.iirel_substrate [in set4]
Relation.inc_all_equivalence_relations [in set4]
Relation.inc_all_relations [in set4]
Relation.inc_arg1_substrate [in set4]
Relation.inc_arg2_substrate [in set4]
Relation.inc_class [in set4]
Relation.inc_class_quotient [in set4]
Relation.inc_coarse_all_equivalence_relations [in set4]
Relation.inc_in_quotient_substrate [in set4]
Relation.inc_itself_class [in set4]
Relation.inc_pr1_substrate [in set4]
Relation.inc_pr2_substrate [in set4]
Relation.inc_quotient [in set4]
Relation.inc_rep_itself [in set4]
Relation.inc_rep_substrate [in set4]
Relation.inc_substrate [in set4]
Relation.inc_substrate_rw [in set4]
Relation.induced_rel_class [in set4]
Relation.induced_rel_equivalence [in set4]
Relation.induced_rel_iirel_axioms [in set4]
Relation.induced_rel_related [in set4]
Relation.induced_rel_substrate [in set4]
Relation.inter2_is_graph1 [in set4]
Relation.inter2_is_graph2 [in set4]
Relation.inter_rel_equivalence [in set4]
Relation.inter_rel_graph [in set4]
Relation.inter_rel_reflexive [in set4]
Relation.inter_rel_rw [in set4]
Relation.inter_rel_substrate [in set4]
Relation.inter_rel_symmetric [in set4]
Relation.inter_rel_transitive [in set4]
Relation.in_class_related [in set4]
Relation.isc_equivalence [in set4]
Relation.isc_reflexive [in set4]
Relation.isc_symmetric [in set4]
Relation.isc_transitive [in set4]
Relation.is_class_class [in set4]
Relation.is_class_pr [in set4]
Relation.is_class_rw [in set4]
Relation.nonempty_class_symmetric [in set4]
Relation.nonempty_image [in set4]
Relation.non_empty_in_quotient [in set4]
Relation.partition_class_inc [in set4]
Relation.partition_from_equivalence [in set4]
Relation.partition_fun_bijective [in set4]
Relation.partition_is_equivalence [in set4]
Relation.partition_relation_class [in set4]
Relation.partition_relation_class2 [in set4]
Relation.partition_relation_pr [in set4]
Relation.partition_relation_substrate [in set4]
Relation.partition_rel_graph [in set4]
Relation.prod_of_rel_is_rel [in set4]
Relation.prod_of_rel_pr [in set4]
Relation.prod_of_rel_refl [in set4]
Relation.prod_of_rel_sym [in set4]
Relation.prod_of_rel_trans [in set4]
Relation.quotient_canonical_decomposition [in set4]
Relation.quotient_of_relations_class_bis [in set4]
Relation.quotient_of_relations_equivalence [in set4]
Relation.quotient_of_relations_pr [in set4]
Relation.quotient_of_relations_related [in set4]
Relation.quotient_of_relations_related_bis [in set4]
Relation.quotient_of_relations_substrate [in set4]
Relation.reflexive_ap [in set4]
Relation.reflexive_ap2 [in set4]
Relation.reflexive_inc_substrate [in set4]
Relation.reflexive_reflexive [in set4]
Relation.reflexivity_e [in set4]
Relation.related_class_eq [in set4]
Relation.related_class_eq1 [in set4]
Relation.related_ext_to_prod_rel [in set4]
Relation.related_e_rw [in set4]
Relation.related_graph_canon_proj [in set4]
Relation.related_prod_of_rel1 [in set4]
Relation.related_prod_of_rel2 [in set4]
Relation.related_rep_class [in set4]
Relation.related_rep_in_class [in set4]
Relation.related_rep_rep [in set4]
Relation.related_rw [in set4]
Relation.rel_on_quo_pr [in set4]
Relation.rel_on_quo_pr2 [in set4]
Relation.rep_sys_function_pr [in set4]
Relation.rep_sys_function_pr2 [in set4]
Relation.right_inv_canon_proj [in set4]
Relation.saturated_complement [in set4]
Relation.saturated_intersection [in set4]
Relation.saturated_pr [in set4]
Relation.saturated_pr2 [in set4]
Relation.saturated_pr3 [in set4]
Relation.saturated_pr4 [in set4]
Relation.saturated_union [in set4]
Relation.saturation_of_pr [in set4]
Relation.saturation_of_smallest [in set4]
Relation.saturation_of_union [in set4]
Relation.section_canon_proj_axioms [in set4]
Relation.section_canon_proj_function [in set4]
Relation.section_canon_proj_pr [in set4]
Relation.section_canon_proj_W [in set4]
Relation.section_is_representative_system_function [in set4]
Relation.selfinverse_graph_symmetric [in set4]
Relation.substrate_prod_of_rel [in set4]
Relation.substrate_prod_of_rel1 [in set4]
Relation.substrate_prod_of_rel2 [in set4]
Relation.substrate_smallest [in set4]
Relation.substrate_sub [in set4]
Relation.sub_class_substrate [in set4]
Relation.sub_graph_coarse_substrate [in set4]
Relation.sub_im_canon_proj_quotient [in set4]
Relation.sub_quotient_powerset [in set4]
Relation.surjective_pr7 [in set4]
Relation.symmetricity_e [in set4]
Relation.symmetric_ap [in set4]
Relation.symmetric_symmetric [in set4]
Relation.symmetric_transitive_equivalence [in set4]
Relation.symmetric_transitive_reflexive [in set4]
Relation.transitive_ap [in set4]
Relation.transitive_transitive [in set4]
Relation.transitivity_e [in set4]
Relation.trivial_equiv [in set4]
Relation.union2_is_graph [in set4]
Relation.union_quotient [in set4]
T
Tactics1.seq_deconj [in set1]Tactics1.uneq [in set1]
Tactics1.uneq2 [in set1]
U
Union.inc_tack_on_sub [in set1]Union.inc_tack_on_x [in set1]
Union.inc_tack_on_y [in set1]
Union.inc_union2_rw [in set1]
Union.sub_union [in set1]
Union.tack_on_complement [in set1]
Union.tack_on_inc [in set1]
Union.tack_on_or [in set1]
Union.tack_on_sub [in set1]
Union.tack_on_when_inc [in set1]
Union.union2comm [in set1]
Union.union2idem [in set1]
Union.union2sub_first [in set1]
Union.union2sub_second [in set1]
Union.union2_first [in set1]
Union.union2_or [in set1]
Union.union2_second [in set1]
Union.union2_sub [in set1]
Union.union_exists [in set1]
Union.union_inc [in set1]
Union.union_sub [in set1]
W
Worder.bij_pair_isomorphism_onto_segment [in set6]Worder.canonical_doubleton_order_pr [in set6]
Worder.coarse_segment_monotone [in set6]
Worder.compose_order_isomorphism [in set6]
Worder.compose_order_morphism [in set6]
Worder.disjoint_union2_rw [in set6]
Worder.disjoint_union2_rw1 [in set6]
Worder.empty_is_segment [in set6]
Worder.identity_isomorphism [in set6]
Worder.identity_morphism [in set6]
Worder.increasing_function_segments [in set6]
Worder.inc_bound_segmentc [in set6]
Worder.inc_lt1_substrate [in set6]
Worder.inc_lt2_substrate [in set6]
Worder.inc_segment [in set6]
Worder.inc_set_of_segments [in set6]
Worder.induced_order_trans [in set6]
Worder.induced_trans [in set6]
Worder.inductive_graphs [in set6]
Worder.inductive_max_greater [in set6]
Worder.inductive_powerset [in set6]
Worder.intersection_is_segment [in set6]
Worder.inverse_order_isomorphism [in set6]
Worder.isomorphic_subset_segment [in set6]
Worder.isomorphism_worder [in set6]
Worder.isomorphism_worder_unique [in set6]
Worder.lexorder_gle [in set6]
Worder.lexorder_order [in set6]
Worder.lexorder_substrate [in set6]
Worder.lexorder_substrate_aux [in set6]
Worder.lexorder_total [in set6]
Worder.le_in_segment [in set6]
Worder.lt_in_segment [in set6]
Worder.maximal_in_powerset [in set6]
Worder.minimal_in_powerset [in set6]
Worder.not_in_segment [in set6]
Worder.not_lt_self [in set6]
Worder.order_merge1 [in set6]
Worder.order_merge2 [in set6]
Worder.order_merge3 [in set6]
Worder.order_merge4 [in set6]
Worder.order_merge5 [in set6]
Worder.order_morphism_pr1 [in set6]
Worder.rts_extensionality [in set6]
Worder.rts_function [in set6]
Worder.rts_surjective [in set6]
Worder.rts_W [in set6]
Worder.segmentc_rw [in set6]
Worder.segment_alt [in set6]
Worder.segment_alt1 [in set6]
Worder.segment_c_pr [in set6]
Worder.segment_dichot_sub [in set6]
Worder.segment_inc [in set6]
Worder.segment_induced [in set6]
Worder.segment_induced1 [in set6]
Worder.segment_induced_a [in set6]
Worder.segment_injective [in set6]
Worder.segment_injective1 [in set6]
Worder.segment_is_segment [in set6]
Worder.segment_monotone [in set6]
Worder.segment_rw [in set6]
Worder.set_of_segments_axiom [in set6]
Worder.set_of_segments_iso_bijective [in set6]
Worder.set_of_segments_iso_isomorphism [in set6]
Worder.set_of_segments_worder [in set6]
Worder.singleton_emptyset_not_empty [in set6]
Worder.singleton_pr1 [in set6]
Worder.strict_increasing_extens [in set6]
Worder.subsegment_is_segment [in set6]
Worder.substrate_canonical_doubleton_order [in set6]
Worder.substrate_is_segment [in set6]
Worder.sub_segment [in set6]
Worder.sub_segmentc [in set6]
Worder.sub_segment1 [in set6]
Worder.sub_segment2 [in set6]
Worder.sub_set_of_segments [in set6]
Worder.tack_on_segment [in set6]
Worder.transfinite_aux1 [in set6]
Worder.transfinite_aux2 [in set6]
Worder.transfinite_aux3 [in set6]
Worder.transfinite_defined_pr [in set6]
Worder.transfinite_definition [in set6]
Worder.transfinite_definition_stable [in set6]
Worder.transfinite_pr [in set6]
Worder.transfinite_principle [in set6]
Worder.transfinite_principle1 [in set6]
Worder.transfinite_principle2 [in set6]
Worder.transfinite_principle_bis [in set6]
Worder.transfinite_unique [in set6]
Worder.transfinite_unique1 [in set6]
Worder.unionf_is_segment [in set6]
Worder.union_is_segment [in set6]
Worder.union_segments [in set6]
Worder.unique_isomorphism_onto_segment [in set6]
Worder.well_ordered_segment [in set6]
Worder.wordering_pr [in set6]
Worder.worder_adjoin_greatest [in set6]
Worder.worder_canonical_doubleton_order [in set6]
Worder.worder_hassup [in set6]
Worder.worder_least [in set6]
Worder.worder_merge [in set6]
Worder.worder_restriction [in set6]
Worder.worder_total [in set6]
Worder.Zermelo [in set6]
Worder.Zermelo_aux [in set6]
Worder.Zermelo_aux0 [in set6]
Worder.Zermelo_aux1 [in set6]
Worder.Zermelo_aux2 [in set6]
Worder.Zermelo_aux3 [in set6]
Worder.Zermelo_aux4 [in set6]
Worder.Zermelo_bis [in set6]
Worder.Zorn_aux [in set6]
Worder.Zorn_lemma [in set6]
Constructor Index
A
Axioms.nonemptyT_intro [in set1]Axioms.nonempty_intro [in set1]
C
Constructions.Zorec_c [in set1]I
IntegerProps.list_prop_cons [in set9]IntegerProps.list_prop_nil [in set9]
L
Little.one_point_intro [in set1]Little.two_points_a [in set1]
Little.two_points_b [in set1]
Inductive Index
A
Axioms.nonempty [in set1]Axioms.nonemptyT [in set1]
B
Bfunction.functionT [in set2]Bunion.Uintegral [in set3]
C
Constructions.emptyset [in set1]Constructions.Zorec [in set1]
I
IntegerProps.list_prop [in set9]L
Little.one_point [in set1]Little.two_points [in set1]
U
Union.Union_integral [in set1]Definition Index
A
Axioms.inc [in set1]Axioms.sub [in set1]
B
Bfunction.agreeC [in set2]Bfunction.agrees_on [in set2]
Bfunction.bcreate [in set2]
Bfunction.bcreate1 [in set2]
Bfunction.bijective [in set2]
Bfunction.bijectiveC [in set2]
Bfunction.BL [in set2]
Bfunction.canonical_injection [in set2]
Bfunction.composable [in set2]
Bfunction.composeC [in set2]
Bfunction.constant_function [in set2]
Bfunction.constant_functionC [in set2]
Bfunction.corresp_functionT [in set2]
Bfunction.diagonal_application [in set2]
Bfunction.empty_function [in set2]
Bfunction.empty_functionC [in set2]
Bfunction.equipotent [in set2]
Bfunction.extends [in set2]
Bfunction.extendsC [in set2]
Bfunction.ext_to_prod [in set2]
Bfunction.ext_to_prodC [in set2]
Bfunction.first_proj [in set2]
Bfunction.functional_graph [in set2]
Bfunction.functionT_fun [in set2]
Bfunction.identityC [in set2]
Bfunction.imageC [in set2]
Bfunction.inclusionC [in set2]
Bfunction.injective [in set2]
Bfunction.injectiveC [in set2]
Bfunction.inverseC [in set2]
Bfunction.inv_graph_canon [in set2]
Bfunction.is_constant_function [in set2]
Bfunction.is_constant_functionC [in set2]
Bfunction.is_function [in set2]
Bfunction.is_left_inverse [in set2]
Bfunction.is_left_inverseC [in set2]
Bfunction.is_right_inverse [in set2]
Bfunction.is_right_inverseC [in set2]
Bfunction.left_inverseC [in set2]
Bfunction.pairC [in set2]
Bfunction.partial_fun1 [in set2]
Bfunction.partial_fun2 [in set2]
Bfunction.pr1C [in set2]
Bfunction.pr2C [in set2]
Bfunction.restriction [in set2]
Bfunction.restrictionC [in set2]
Bfunction.restriction1 [in set2]
Bfunction.restriction2 [in set2]
Bfunction.restriction2C [in set2]
Bfunction.restriction2_axioms [in set2]
Bfunction.restriction_to_image [in set2]
Bfunction.right_inverseC [in set2]
Bfunction.second_proj [in set2]
Bfunction.small_set [in set2]
Bfunction.surjective [in set2]
Bfunction.surjectiveC [in set2]
Bfunction.tack_on_f [in set2]
Bfunction.transf_axioms [in set2]
Bfunction.W [in set2]
Bfunction.WT [in set2]
Border.antisymmetric_r [in set5]
Border.bounded_above [in set5]
Border.bounded_below [in set5]
Border.bounded_both [in set5]
Border.coarser [in set5]
Border.coarser_preorder [in set5]
Border.cofinal_set [in set5]
Border.coinitial_set [in set5]
Border.cst_graph [in set5]
Border.decreasing_fun [in set5]
Border.empty_function_tg [in set5]
Border.equivalence_associated_o [in set5]
Border.extension_order [in set5]
Border.fam_of_substrates [in set5]
Border.function_order [in set5]
Border.function_order_r [in set5]
Border.gge [in set5]
Border.ggt [in set5]
Border.gle [in set5]
Border.glt [in set5]
Border.graph_of_function [in set5]
Border.graph_of_partition [in set5]
Border.graph_order [in set5]
Border.graph_order_r [in set5]
Border.greatest_element [in set5]
Border.greatest_lower_bound [in set5]
Border.has_infimum [in set5]
Border.has_inf_graph [in set5]
Border.has_supremum [in set5]
Border.has_sup_graph [in set5]
Border.inclusion_order [in set5]
Border.inclusion_suborder [in set5]
Border.increasing_fun [in set5]
Border.induced_order [in set5]
Border.inf [in set5]
Border.infimum [in set5]
Border.inf_graph [in set5]
Border.interval_cc [in set5]
Border.interval_co [in set5]
Border.interval_cu [in set5]
Border.interval_oc [in set5]
Border.interval_oo [in set5]
Border.interval_ou [in set5]
Border.interval_uc [in set5]
Border.interval_uo [in set5]
Border.interval_uu [in set5]
Border.is_antisymmetric [in set5]
Border.is_bounded_interval [in set5]
Border.is_closed_interval [in set5]
Border.is_inf_fun [in set5]
Border.is_inf_graph [in set5]
Border.is_interval [in set5]
Border.is_left_unbounded_interval [in set5]
Border.is_lu_interval [in set5]
Border.is_open_interval [in set5]
Border.is_right_unbounded_interval [in set5]
Border.is_ru_interval [in set5]
Border.is_semi_open_interval [in set5]
Border.is_sup_fun [in set5]
Border.is_sup_graph [in set5]
Border.is_unbounded_interval [in set5]
Border.lattice [in set5]
Border.least_element [in set5]
Border.least_upper_bound [in set5]
Border.left_directed [in set5]
Border.lower_bound [in set5]
Border.maximal_element [in set5]
Border.minimal_element [in set5]
Border.monotone_fun [in set5]
Border.opposite_order [in set5]
Border.opposite_relation [in set5]
Border.order [in set5]
Border.order_associated [in set5]
Border.order_axioms [in set5]
Border.order_isomorphism [in set5]
Border.order_morphism [in set5]
Border.order_r [in set5]
Border.order_re [in set5]
Border.order_with_greatest [in set5]
Border.partial_fun [in set5]
Border.partition_fun_of_set [in set5]
Border.partition_relation_set [in set5]
Border.partition_relation_set_aux [in set5]
Border.preorder [in set5]
Border.preorder_r [in set5]
Border.product2_order [in set5]
Border.product_order [in set5]
Border.product_order_axioms [in set5]
Border.product_order_r [in set5]
Border.prod_of_substrates [in set5]
Border.reflexive_rr [in set5]
Border.right_directed [in set5]
Border.set_of_fgraphs [in set5]
Border.set_of_majorants1 [in set5]
Border.set_of_partition_set [in set5]
Border.set_of_preorders [in set5]
Border.strict_decreasing_fun [in set5]
Border.strict_increasing_fun [in set5]
Border.strict_monotone_fun [in set5]
Border.sup [in set5]
Border.supremum [in set5]
Border.sup_graph [in set5]
Border.the_greatest_element [in set5]
Border.the_least_element [in set5]
Border.total_order [in set5]
Border.upper_bound [in set5]
Bproduct.constant_functor [in set3]
Bproduct.constant_graph [in set3]
Bproduct.diagonal_graphp [in set3]
Bproduct.ext_map_prod [in set3]
Bproduct.ext_map_prod_aux [in set3]
Bproduct.ext_map_prod_axioms [in set3]
Bproduct.fun_set_to_prod [in set3]
Bproduct.fun_set_to_prod5 [in set3]
Bproduct.gbcreate [in set3]
Bproduct.is_constant_graph [in set3]
Bproduct.is_singleton [in set3]
Bproduct.productb [in set3]
Bproduct.productf [in set3]
Bproduct.productt [in set3]
Bproduct.product1 [in set3]
Bproduct.product1_canon [in set3]
Bproduct.product2 [in set3]
Bproduct.product2_canon [in set3]
Bproduct.product_compose [in set3]
Bproduct.prod_assoc_axioms [in set3]
Bproduct.prod_assoc_map [in set3]
Bproduct.prod_of_function [in set3]
Bproduct.prod_of_products [in set3]
Bproduct.prod_of_products_canon [in set3]
Bproduct.prod_of_product_aux [in set3]
Bproduct.prod_of_prod_target [in set3]
Bproduct.pr_i [in set3]
Bproduct.pr_it [in set3]
Bproduct.pr_j [in set3]
Bproduct.restriction_product [in set3]
Bunion.coarser_c [in set3]
Bunion.coarser_covering [in set3]
Bunion.compose3function [in set3]
Bunion.covering [in set3]
Bunion.covering_f [in set3]
Bunion.covering_s [in set3]
Bunion.disjoint [in set3]
Bunion.disjoint_union [in set3]
Bunion.disjoint_union_fam [in set3]
Bunion.extension_to_parts [in set3]
Bunion.first_partial_fun [in set3]
Bunion.first_partial_function [in set3]
Bunion.first_partial_map [in set3]
Bunion.function_prop [in set3]
Bunion.function_prop_sub [in set3]
Bunion.injective_graph [in set3]
Bunion.intersectionb [in set3]
Bunion.intersectionf [in set3]
Bunion.intersectiont [in set3]
Bunion.intersection_covering [in set3]
Bunion.intersection_covering2 [in set3]
Bunion.largest_partition [in set3]
Bunion.mutually_disjoint [in set3]
Bunion.partial_fun_axioms [in set3]
Bunion.partition [in set3]
Bunion.partition_fam [in set3]
Bunion.partition_s [in set3]
Bunion.partition_with_complement [in set3]
Bunion.second_partial_fun [in set3]
Bunion.second_partial_function [in set3]
Bunion.second_partial_map [in set3]
Bunion.set_of_functions [in set3]
Bunion.set_of_gfunctions [in set3]
Bunion.set_of_permutations [in set3]
Bunion.set_of_sub_functions [in set3]
Bunion.smallest_partition [in set3]
Bunion.unionb [in set3]
Bunion.unionf [in set3]
Bunion.uniont [in set3]
Bunion.variant [in set3]
Bunion.variantL [in set3]
Bunion.variantLc [in set3]
C
Cardinal.cardinal [in set7]Cardinal.cardinal_le [in set7]
Cardinal.cardinal_lt [in set7]
Cardinal.cardinal_prod [in set7]
Cardinal.cardinal_sum [in set7]
Cardinal.card_mult [in set7]
Cardinal.card_one [in set7]
Cardinal.card_plus [in set7]
Cardinal.card_pow [in set7]
Cardinal.card_two [in set7]
Cardinal.card_zero [in set7]
Cardinal.doubleton_fam [in set7]
Cardinal.equipotent_to_subset [in set7]
Cardinal.is_cardinal [in set7]
Cardinal.restriction_to_image [in set7]
Cardinal.set_of_cardinals_le [in set7]
Cardinal.TPas [in set7]
Cardinal.TPbs [in set7]
Cartesian.product [in set1]
Complement.complement [in set1]
Constructions.Bo [in set1]
Constructions.by_cases [in set1]
Constructions.choose [in set1]
Constructions.choosenat [in set1]
Constructions.cut [in set1]
Constructions.cut_to [in set1]
Constructions.empty [in set1]
Constructions.exists_unique [in set1]
Constructions.rep [in set1]
Constructions.strict_sub [in set1]
Constructions.Xo [in set1]
Constructions.Yo [in set1]
Constructions.Yt [in set1]
Constructions.Yy [in set1]
Constructions.Zo [in set1]
Correspondence.acreate [in set2]
Correspondence.composableC [in set2]
Correspondence.compose [in set2]
Correspondence.compose_graph [in set2]
Correspondence.corresp [in set2]
Correspondence.corr_propb [in set2]
Correspondence.diagonal [in set2]
Correspondence.gacreate [in set2]
Correspondence.graph [in set2]
Correspondence.identity [in set2]
Correspondence.image_by_fun [in set2]
Correspondence.image_by_graph [in set2]
Correspondence.image_of_fun [in set2]
Correspondence.im_singleton [in set2]
Correspondence.inverse_fun [in set2]
Correspondence.inverse_graph [in set2]
Correspondence.inv_image_by_fun [in set2]
Correspondence.inv_image_by_graph [in set2]
Correspondence.is_correspondence [in set2]
Correspondence.is_triple [in set2]
Correspondence.related [in set2]
Correspondence.set_of_correspondences [in set2]
Correspondence.source [in set2]
Correspondence.target [in set2]
F
FiniteSets.Bnat [in set8]FiniteSets.Bnat_le [in set8]
FiniteSets.Bnat_lt [in set8]
FiniteSets.Bnat_order [in set8]
FiniteSets.cardinal_nat [in set8]
FiniteSets.card_four [in set8]
FiniteSets.card_three [in set8]
FiniteSets.decent_set [in set8]
FiniteSets.infinite_set [in set8]
FiniteSets.is_finite_c [in set8]
FiniteSets.is_finite_set [in set8]
FiniteSets.is_infinite_c [in set8]
FiniteSets.natR [in set8]
FiniteSets.nat_to_B [in set8]
FiniteSets.of_finite_character [in set8]
FiniteSets.pow [in set8]
FiniteSets.predc [in set8]
FiniteSets.pseudo_ordinal [in set8]
FiniteSets.set_of_finite_subsets [in set8]
FiniteSets.set_of_finite_subsets_prop [in set8]
FiniteSets.succ [in set8]
FiniteSets.transitive_set [in set8]
Function.domain [in set1]
Function.fcomposable [in set1]
Function.fcompose [in set1]
Function.fgraph [in set1]
Function.gcompose [in set1]
Function.graph_constructor [in set1]
Function.identity_g [in set1]
Function.inverse_image [in set1]
Function.is_graph [in set1]
Function.is_restriction [in set1]
Function.range [in set1]
Function.restr [in set1]
Function.tcreate [in set1]
I
Image.fun_image [in set1]InfiniteSets.decreasing_sequence [in set10]
InfiniteSets.increasing_sequence [in set10]
InfiniteSets.induction_defined [in set10]
InfiniteSets.induction_defined0 [in set10]
InfiniteSets.induction_defined0_set [in set10]
InfiniteSets.induction_defined1 [in set10]
InfiniteSets.induction_defined1_set [in set10]
InfiniteSets.induction_defined_set [in set10]
InfiniteSets.is_countable_set [in set10]
InfiniteSets.stationary_sequence [in set10]
IntegerProps.back_to_nat [in set9]
IntegerProps.binom [in set9]
IntegerProps.Bnat_divides [in set9]
IntegerProps.card_quo [in set9]
IntegerProps.card_rem [in set9]
IntegerProps.card_sub [in set9]
IntegerProps.card_sub0 [in set9]
IntegerProps.char_fun [in set9]
IntegerProps.contraction [in set9]
IntegerProps.division_prop [in set9]
IntegerProps.expansion_value [in set9]
IntegerProps.factorial [in set9]
IntegerProps.factorialC [in set9]
IntegerProps.fct_prod [in set9]
IntegerProps.fct_sum [in set9]
IntegerProps.fct_to_list [in set9]
IntegerProps.fct_to_listB [in set9]
IntegerProps.fct_to_listB1 [in set9]
IntegerProps.fct_to_list_rev [in set9]
IntegerProps.finite_int_fam [in set9]
IntegerProps.function_on_nat [in set9]
IntegerProps.iid_function [in set9]
IntegerProps.interval_Bnat [in set9]
IntegerProps.interval_Bnatco [in set9]
IntegerProps.interval_Bnato [in set9]
IntegerProps.interval_co_0a [in set9]
IntegerProps.is_expansion [in set9]
IntegerProps.list_prod [in set9]
IntegerProps.list_range [in set9]
IntegerProps.list_subset [in set9]
IntegerProps.list_sum [in set9]
IntegerProps.list_to_f [in set9]
IntegerProps.list_to_fB [in set9]
IntegerProps.list_to_fct [in set9]
IntegerProps.list_to_fctB [in set9]
IntegerProps.Ndivides [in set9]
IntegerProps.Nquo [in set9]
IntegerProps.Nrem [in set9]
IntegerProps.number_of_injections [in set9]
IntegerProps.O [in set9]
IntegerProps.partition_with_pi_elements [in set9]
IntegerProps.rest_minus_interval [in set9]
IntegerProps.rest_plus_interval [in set9]
IntegerProps.set_of_functions_sum_eq [in set9]
IntegerProps.set_of_functions_sum_le [in set9]
IntegerProps.set_of_functions_sum_le_int [in set9]
IntegerProps.set_of_increasing_functions_int [in set9]
IntegerProps.set_of_injections [in set9]
IntegerProps.set_of_partitions [in set9]
IntegerProps.set_of_partitions_aux [in set9]
IntegerProps.subsets_with_p_elements [in set9]
IntegerProps.sum_to_increasing_fct [in set9]
IntegerProps.sum_to_increasing_fun [in set9]
Intersection.intersection [in set1]
Intersection.intersection2 [in set1]
L
Little.doubleton [in set1]Little.singleton [in set1]
Little.TPa [in set1]
Little.TPb [in set1]
O
Ordinals.canonical_du2 [in set11]Ordinals.is_order_type [in set11]
Ordinals.is_ordinal [in set11]
Ordinals.order_isomorphic [in set11]
Ordinals.order_type [in set11]
Ordinals.order_type_le [in set11]
Ordinals.ordinal_product2 [in set11]
Ordinals.ordinal_sum [in set11]
Ordinals.ordinal_sum2 [in set11]
Ordinals.ordinal_sum_assoc [in set11]
Ordinals.ordinal_sum_assoc_aux [in set11]
Ordinals.ordinal_sum_axioms [in set11]
Ordinals.ordinal_sum_axioms1 [in set11]
Ordinals.ordinal_sum_r [in set11]
Ordinals.ord_omega [in set11]
Ordinals.ord_one [in set11]
Ordinals.ord_prod [in set11]
Ordinals.ord_prod2 [in set11]
Ordinals.ord_sum [in set11]
Ordinals.ord_sum2 [in set11]
Ordinals.ord_two [in set11]
Ordinals.ord_zero [in set11]
Ordinals.sum_of_substrates [in set11]
P
Pair.bpair_x [in set1]Pair.is_kpair [in set1]
Pair.is_pair [in set1]
Pair.kpair [in set1]
Pair.kpr1 [in set1]
Pair.kpr2 [in set1]
Pair.P [in set1]
Pair.pair_first [in set1]
Pair.pair_second [in set1]
Pair.Q [in set1]
Pair.V [in set1]
Powerset.powerset [in set1]
R
Relation.all_equivalence_relations [in set4]Relation.all_relations [in set4]
Relation.canonical_foq_induced_rel [in set4]
Relation.canon_proj [in set4]
Relation.class [in set4]
Relation.coarse [in set4]
Relation.compatible_with_equiv [in set4]
Relation.compatible_with_equivs [in set4]
Relation.compatible_with_equiv_p [in set4]
Relation.equivalence_associated [in set4]
Relation.equivalence_r [in set4]
Relation.equivalence_re [in set4]
Relation.eq_rel_associated [in set4]
Relation.finer_axioms [in set4]
Relation.finer_equivalence [in set4]
Relation.first_proj_eq [in set4]
Relation.first_proj_eqr [in set4]
Relation.function_on_quotient [in set4]
Relation.function_on_quotients [in set4]
Relation.fun_on_quotient [in set4]
Relation.fun_on_quotients [in set4]
Relation.fun_on_rep [in set4]
Relation.fun_on_reps [in set4]
Relation.graph_on [in set4]
Relation.iirel_axioms [in set4]
Relation.induced_relation [in set4]
Relation.induced_rel_axioms [in set4]
Relation.inverse_direct_value [in set4]
Relation.inv_image_relation [in set4]
Relation.in_same_coset [in set4]
Relation.is_class [in set4]
Relation.is_equivalence [in set4]
Relation.is_graph_of [in set4]
Relation.is_reflexive [in set4]
Relation.is_symmetric [in set4]
Relation.is_transitive [in set4]
Relation.partition_relation [in set4]
Relation.prod_of_relation [in set4]
Relation.quotient [in set4]
Relation.quotient_of_relations [in set4]
Relation.reflexive_r [in set4]
Relation.relation_on_quotient [in set4]
Relation.representative_system [in set4]
Relation.representative_system_function [in set4]
Relation.restricted_eq [in set4]
Relation.saturated [in set4]
Relation.saturation_of [in set4]
Relation.section_canon_proj [in set4]
Relation.substrate [in set4]
Relation.substrate_for_prod [in set4]
Relation.symmetric_r [in set4]
Relation.transitive_r [in set4]
Relation.union_image [in set4]
U
Union.tack_on [in set1]Union.union [in set1]
Union.union2 [in set1]
W
Worder.canonical_doubleton_order [in set6]Worder.common_extension_order [in set6]
Worder.common_extension_order_axiom [in set6]
Worder.common_ordering_set [in set6]
Worder.common_worder_axiom [in set6]
Worder.inductive_set [in set6]
Worder.is_segment [in set6]
Worder.lexicographic_order [in set6]
Worder.lexicographic_order_axioms [in set6]
Worder.lexicographic_order_r [in set6]
Worder.restriction_to_segment [in set6]
Worder.restriction_to_segment_axiom [in set6]
Worder.segment [in set6]
Worder.segment_c [in set6]
Worder.set_of_segments [in set6]
Worder.set_of_segments_iso [in set6]
Worder.set_of_segments_strict [in set6]
Worder.transfinite_def [in set6]
Worder.transfinite_defined [in set6]
Worder.worder [in set6]
Worder.worder_r [in set6]
Worder.Zermelo_axioms [in set6]
Module Index
A
Axioms [in set1]B
Bfunction [in set2]Border [in set5]
Bproduct [in set3]
Bunion [in set3]
C
Cardinal [in set7]Cartesian [in set1]
Complement [in set1]
Constructions [in set1]
Correspondence [in set2]
F
FiniteSets [in set8]Function [in set1]
I
Image [in set1]InfiniteSets [in set10]
IntegerProps [in set9]
Intersection [in set1]
L
Little [in set1]O
Ordinals [in set11]P
Pair [in set1]Powerset [in set1]
R
Relation [in set4]T
Tactics1 [in set1]U
Union [in set1]W
Worder [in set6]Library Index
S
set1set10
set11
set2
set3
set4
set5
set6
set7
set8
set9
| Global Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (3100 entries) |
| Axiom Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (13 entries) |
| Lemma Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (2517 entries) |
| Constructor Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (8 entries) |
| Inductive Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (10 entries) |
| Definition Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (517 entries) |
| Module Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (24 entries) |
| Library Index | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z | _ | (11 entries) |
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