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L E    }      @Is @ 1q @ 1 @ 1 @ 1 @ 8 @ sp @ yp @ ~pƩ @ p @ pG @ p:@@R@@k,mul_shuffle2 @  v g     @ 9 ܠ ՠ x q b   ޠ@J˚ @ 1ɚ @ 1  @ 1 @ 1 @ 8@ p @ pީ@ p @ p@ p@ p@@@@à,mul_shuffle3 @ ޠ Π  b Y     4 - Р ɠ  _ G 6YL>@WK #A@@1 !F@E1bK@J1P@J8V@ p \@ $p la@ )p qg@ /pې@@@@ %le_wd @'   E >  ڠ } v      @@A&NZBase'NZOrder&NatInt'Numbers#Coq@ ) '@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp 8 6@A@@@@"NZ - ,@A@@@@1@@1,@1@@17@8)@1A@8 ꚠ@ 9 @@Z@@AA@@A@*lt_le_incl @r    K D    | m   j]O@hA ֚@1 Ԛ@1@@"lt9 @ 9  @@@@@7'le_refl @ŠI@  ܠ  x      F . @B (@'1-@ 9  < <@@ 1@@`.lt_succ_diag_r @ޠϠri    D =  ٠ ʠ o W FǠ@C 3Q@P1V@W9 e\@ 技 @@@@@.le_succ_diag_r @ :3 ֠ Ϡ r k      t@D a@~1@ c9  @ 9技 Ð@@@@@/neq_succ_diag_l @J:+ΠŠha    < 5 & ˠ  #@!E @1 @8@ i技  Ȑ@@ @@젠/neq_succ_diag_r @zj[4- Р ɠ l e V   ҠSF8@QF @1 @8 󩚠@ 技 #@@@@@/nlt_succ_diag_l @.%Ƞd]     +  vh@G  @ 1 吩@9@ 技 S (@@@@@L/nle_succ_diag_l @ڠʠ^U0) ̠ Š  [ C 2@H =@<1 D@ #9 J@ 技  X@@@@@|)le_succ_l @ (!Ġ`Y     s b֠@I Om@l1 Mr@q1 y@ X9 @ .技  @9 @@ @@+le_gt_cases @D4%Ƞb[6/  Š  @J @1 @1 @"or @@ 9  ɩ@9 Ɛ@@ J@@-lt_trichotomy @~n_81Ԡ͠piZ   ֠WJ<@UK Ú@1 @1:@9 A@8 @9 @@@@@+(lt_asymm @=4נРsl:"w@L @1 !@ 1@'@(9 7 .@/9 @@ a@@`(lt_trans @ޠϠri D=٠ʠoWFǠ@M 3Q@P1 1V@U1r[@Z1@a@b9 @g@h9 l@m9  1@@ @@(le_trans @-KD| @N r@1 p@1@1@@9  /@@9  5@9 ?@@ 7@@ݠ+lt_strorder @k[L%]VGԠàD7)@BO@+StrictOrder.[@@1@9@@ @@ +le_preorder @zSLureW@pP @(PreOrder@@1@9 @@ @@9/le_partialorder @ǠKBޠzH0@Q7@,PartialOrder5͛К0@/14@.88@-{<@9 [@b(瀐@@@ s@A @E@FAhCV@ABC@@y)lt_compat @U@%lt_wdϦ@ ̰@]@\1@b@a1 ݩ h@g1@m@l1 蚠q@k8 w@v1 򚠐{@u8 @9@@@%lt_wd']ɠA1"Š_X3,  @@@@@Р(lt_total @@L%׀@ @1 @1 @9 ͩ@8 ԩ@9 ѐJ3@ aǠvg @9ܠՠxqbޠ_RD@@@@@'le_lteq @@+lt_eq_cases﯀@ ٚ@1 ך@1@9 W @ 9@ 8@+lt_eq_cases&yˠOF~!L4#@@@@@Z0Private_OrderTacLA'IsTotalT A1 @D@9{@W@+Equivalence~@P@O1T@N8@(eq_equiv7L.'ʠàf_yhܠ@@@@@ @@<άn@@1@9@,Q^?/ à]V1* @@@@@ΠU @@]~k@ @@1@@1 0 @1@@1 ;@8 -@1 E@8@9S{lE>ڠ}vg dWI@@@@@J @@RG#@ܚ@1ښ@1S@9Z @8@9IˠOF~!L4#@@@@@ZE @P@Mrm@:@91?@>1`F@%9 VM@N9]R@L8bC )"ŠaZtcנ@@@@@@@@@"A@#TacGA @1!OH#  @@D!P)OrdersTac*Structures#Coq@rk@@@A@@C!O@@&@ @!t&J@@A@A&a@@"eq&a^@@A@&@ @"le&ڠh@@A@AB&@@"lt&h@@A@&̌@@#one&̌T@@A@A&̔I@@#two&̔IT@@A@&H@@$pred&Hd@@A@&؝[@"@$succ&؝[r@@A@&C@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBo?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@6 @ 1@ 8@@@@AA@@A@ @ӠàWN)"ŠT<+]VP5@Af<@;1A@ 9 @@D@@0)lt_irrefl @|WPݠjYڠ͠Р~c@Bj@i1Bq@r9D@@t@@`g @0 NG"  @CÚ@1@1@@8@8n@@@@*le_antisym @iYJ#[TEҠB5'8(@9D@1@1@@9 @@9 @8 @@@@נ @+"ŠaZ(sevf1*$ @wE:@18@1@@8-$@8@@@@@*interp_ord @!o)OrdersTac3@#ordȠ@ @@@@@@@@@@@D@F@E1@K@J1YP@J8T@U9X@79 @*(@^@]1@c@b1ސ +k= R'6'6'6''+k+7T'+7T'6'ࠒA̠ܠ۠@@"lt\ @@"eq8L@lР@TȠ@@QPO@@A@B@A@xA܀M=.ѠȠkd?8)Π&  נРʠ@@@@@%trans @p`Q*#Ơb[L٠ȠI<.?/@@F"o'@1@1~@1@ @9ON:@@9ON @9ON@)trans_ord-0uGDR̐@@;@@ @@@1>@1 @1B@r 3МA:9@Z0@/1X5@41њ:@91@@@:8϶@F@@8թK@E8ߐ L+k() LL7#'S@$t-&ɠ e^xg۠͠ޠΠq@@@@@a @@1@1!@1d"@ 3МbCY@Ě@1š@1;@1@@9 9@@9 ?@9 I L+k() NN7#'jtueV/(ˠĠg`Qޠ͠ N A 3D4@@@@@Ǡ @@1@1@1@B 3МB  @*@1(@1 @ 1@@ 9@@ 9@ 9 L+k() MM7#'Аt۠ˠ_V1*͠Ơ\D3   e^X=@@@@@-+le_lt_trans @wM@L1uR@Q1W@V1y1@ 3g#nm@d@c1i@h1n@m1@t@S9 @z@ {9 @ 9 L+k() MN7#'4t?/ à]V1*   ɠ @@@@@+lt_le_trans @ۚ@1ٚ@1R@1S@  31@򚠐@1𚠐@1i@1@@ 9g@@9 m@ 9w L+k() NM7#'t']V$  | o arb-& @@@@@%eq_lt @?@1=@1@1A@q 3/65@V,@+1T1@01͚6@51@<@68˶@B@ C9ѩG@ H9ې L+k() ML7#'t%]Vp_  Ӡ Š֠Ơi@@@@@Y%lt_eq @y@x1~@}1@1]@ 3cO@@1@11@1@@ 9/@@85@ 9? L+k() LM7#'`tk[L%]VGԠà D 7 ):*@@@@@%eq_le @@1@1~@1 @9 3]@@1@1@1@@8@ @9 @9  L+k() NL7#'ĐtϠSJ%P8'   YRL1@@@@@!%le_eq @kA@@1iF@E1⚠K@J1m%@ 3+ba@X@W1]@\1b@a1@h@G9 @n@h8s@R9   L+k() LN7#'(t3#QJ%   @@@@@&eq_neq @VF7ڠѠtm HA2נ / " %٠Ӡ@&G隠@1皠@1`@1@@8^@@8f@8 r@@@@@͠&neq_eq @"XQz w j \m](!@nH1@1/ @ 1@1@ꐩ@8@@8&@ 8 @@@@@*not_neq_eq @֠Ǡja<5ؠѠ gO>   picH@IyO@N1wT@S1@-/^@X8nc@]8@@@@R)not_ge_lt @#A:ݠ֠yr{   @J@1@1@j@x9 @ 9-@@@@)not_gt_le @^N?٠|uPI:ߠǠ 7 * -۠@.K񚠐@1@1@@ 9ܩ@9 h@@@@@Ƞ)le_neq_lt @zSLu r e WhX#@iL,@1*@1@ @9 @搩@8@ 9@@@@@ @@@@)@@@@@)@<_neq @ޠΠbY4-Рɠ_G6   @ R#A@@1!F@E1@L@ M9\$S@M8@@@@@ &le_neq @1*͠Ơib|k  ߠ @ SXv@u1V{@z1@ 9@#andЖw@@n9 g@8@@@@@ Ƞ*eq_le_incl @VF7ڠѠtm HA2נ/"@-T@1@1@@8ԩ@9 X@@@@@ (lt_stepl @yj C<ߠؠ{te bUG@`U@1@1@1@@ 9@@8@9@@@@@9(lt_stepr @ǠKBޠzH0@VT*@)1R/@.1˚4@31@:@;9ɶ@@@:8ϩE@F9 ِ@@@@@w(le_stepl @#[Tn]ޠѠ@Wh@g1m@l1 r@q1@x@W9 @~@x8@b9 @@@@@(le_stepr @C3$ǠaZ5.Ġ@XК@1Κ@1G@1@@9 E@@8K@9  U@@@@@ @pa:3֠Ϡrk\ؠYL>@WYŚ@1Ú@1@1@@9 @@9@9 @@@@@0\ @A8۠Ԡwp >&{@Z @1%@$1A*@)1@0@19@6@9 ũ;@<9 ϐ@@@@@m+le_antisymm @ܠvQJנ|dSԠǠ@[@^@]1>c@b1@i@H9 y@o@N9 4t@n8I@@@@@)le_succ_r @4$RK& @ \y@1w@1@9 @X技 @9 @8ũ@j技@@@@@)lt_succ_l @{k\5.ѠʠmfWӠTG9@R]@1@1@@9@技.@9@@@@@&,le_le_succ_r @8/Ҡˠng 5 r@^@1@1@"@9 2'@9 쩚-@技l@@@@@_,lt_lt_succ_r @ݠΠqh C<ߠؠɠnVEƠ@_2P@O10U@T1@[@\9k`@a9%f@技@@@@@,succ_lt_mono @&D=٠|u~@`k@1i@1@9@9@O技ߩ@T技ސ@@@@@נ,succ_le_mono @eUF|WPAΠ>1#@@WgŚ @ 1Ú @ 1@ @9 @@ @9 @9!@նǐ@@@5@3@@ABC@@8+lt_ge_cases @ Ơ   J AݠyG/@h !)@!(1 !.@!-1!5@69E!:@9 B@@@@@l+le_ge_cases @   ۠ ~ u  PI֠{cRӠƠ@i?!]@!\1=!b@!a1!i@H9 y!n@M9 v@@@@@+lt_gt_cases @!.!!   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###H#A""ݠ""y"""!!!@w$$@$1t$@$1@$@9b$@$1\$@$1!$@$8o$@!_技驚$@!9 @@@O@A@@蠠,lt_succ_pred @$v$f$W#####0#)"̠"Š"h"a"R!!ߠ!ΠOB4@Mxp$@$1$@$1@$@9$@$8$@!技$@!4 @@@(@A%@t@ @@ABCD@@,&rs_rs' @$$$$>$5#ؠ#Ѡ#t#m## """";"#"x@y@%@%1@%&@%%1%,@%+1%0@%*8 P >̚%5@%41@@ %<@%;1@%B@"!9 @>%K@!技  3%Q@%P1@%W@"69 @ @%^@%]1 >%c@%b1@%i@"H9 c x@%p@q9 5K'H)@@@@(rs'_rs'' @%4%$%$$$R$K#####&##""" @ z@%@%1@%@%1 %@%1!%@%8   F%@%1@ %@%1@%@"9  ˶@ %@%1 %@%1@%@"9  ܶ@%@9 I  %@%1  ƚ%@%1 Ě%@%1@%@"9 "@%@9 ! . ݚ%@%1 ۚ&@%1@&@"9 9@& @ 9 8&@"技 K@@ E@@D%rbase @%Ҡ% %%V%M$$$$$($!#Ġ###S#;#*@{@&6@&51 Қ&;@&:1!#&A@&@1!!&F@&E1@&L@#+9 @&R@S9!| @@@@@)A'A_right @&&%%%%0%)$̠$Š$h$a$####{#jޠ@|@&v@&u1!&{@&z1@!c&@&1!i&@&1!g&@&1@&@#q9 @&@9!]N Ҷ!&@&1@&@#9  @@@@@נ6strong_right_induction @&e&U&F%%%%|%%$$$W$P$A##Π#>1#@<} F@&@&1 D B @@&@&1 L :&@&1 R&@&8!!!w&@&1@!Ț&@&1@&@#9 !@!՚&@&1!Ӛ&@&1@&@#9 1@'@9!0!C.!뚠' @'1@'@#9 ̐@@@!B@A!@#@@ABC@@E/right_induction @&Ӡ&à&&W&N%%%%%)%"$Š$$$T$<$+@~ @'7@'61   @'?@'>1  'E@'D1 'I@'C8"i"W!嚠'N@'M1@ @"7'U@'T1@'[@$:9 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