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U\{Dud5"Šh_:3֠ϠeL;Ԡ~QM@@@@D(eq_trans @@6Equivalence_TransitiveW@@*Transitive++-̐ѐĐTL@W\DvcC<ߠؠ{t|&@@@@*eq_sym_iff @נƠ'ʠd]81"ǠG6@2@9:@@@@AA@@A@'neq_sym @N' à_XIՠĠn]@YA`;a@+ D8@@A@@+(eq_stepl @&ӠvOHq@Bhf!z@k_@mocڐ@@@Aۓό^>@p@AB@@[(succ_inj @VEI@ܠxF-Ơ@C"n1"n2@23@@@V@AAۀߠKl@2@@ABC@@+succ_inj_wd @tE2ՠxo JCߠРu\K@D/-G,@@@@ A8ӠA4Relation_Definitions)Relations @AB@@/succ_inj_wd_neg @q^>7ڠӠvo w!@ E  sҐZ@@@@@۠1central_induction @֠Š&ɠc\70!ƠF5@1F .$A_wd <@@ @ DF@@@@@ 'add_0_r @ĠT-&ɠ e^O۠ʠ@@A&NZBase%NZMul&NatInt'Numbers#Coq@sq@A@%NZMul&NatInt'Numbers#Coq@)NZMulProp@A@@@@"NZwv@A@%NZAdd&NatInt'Numbers#Coq@)NZAddProp/@@@A@@@A&NZBase%NZAdd&NatInt'Numbers#Coq@A@A@@@"NZ+@@,R@2@!t,RJ@@A@A,Y@@"eq,Y^@@A@,@@ @#add,@d@@A@AB,w@@#mul,wd@@A@,@@#one,T@@A@A,@@#sub,d@@A@,@@#two,T@@A@A,@"@$pred,d@@A@,@'@$succ,r@@A@,筷@,@$zero,筷T@@A@ABCDE@A@E@ [  ^  V@@@ {@T@ @ABC@@AA@@A@*add_succ_r @jW70Ӡ̠oh pug@rA    K@@.@@+-add_succ_comm @Ҡ"Š_X3, Π@B  8  9 v(@@U@@R(add_comm @I"ZSDРڠՠĠ@C  _ : ` ><@@}@@z'add_1_l @!Πq JCߠ{l@D   e    @@@@'add_1_r @I8 <3֠Ϡrk9 E8*%@E '   * #  %@@@@ʠ)add_assoc @q`1d[6/ҠˠaH7m`RM<.@9F O ׶  ض!p ۩  V  X Z R@@@@,add_cancel_l @`M-&ɠ e^wf|k]@hG ~   /  g 蠩  ~@@(@@%,add_cancel_r @̠yYR-&Ƞ@H  2  3[ 4      o@@T@@Q,add_shuffle0 @H~!YRCϠ٠Ԡà@I  ^ 9 _ ` > ۠, @@~@@{,add_shuffle1 @"Ϡr KD|m@J   c  !q  k    c ȩ  ^@@@@,add_shuffle2 @TCG>ڠ}vD+PC50@K 2    2  0 8 :  3@@@@ڠ,add_shuffle3 @pA.ѠtkF?̠۠qXG}pb]L>@IL _     Ǡ d ?@@@@'sub_1_r @kX81Ԡ͠pi qvh@sM    }b @@.@@+'mul_0_r @Ҡ"Š_X3, Π@@  5   _ @@R@@AA@@A@*mul_succ_r @I"ZSDР@A  \ 7 ] ;   ٠ Z @@|@@*(mul_comm @  ͠p IBޠzk@B   ^  b ~  `@@@@O/mul_add_distr_r @ E 4 8/Ҡˠng 5 A4&@?C       ͩ & w @@@@x/mul_add_distr_l @ n ] . aX3,ϠȠ^E4j]O@hD I Ѷ  Ҷ ө  0 O 3 *@@@@)mul_assoc @   W D$\Un]x@E r   #  ڠ Y   [* r@@@@ʠ'mul_1_l @    m MF~! @F  #   @@@@@'mul_1_r @  Ӡ   4נΠqj E>/ԠӠ@G  G %  @@d@@,mul_shuffle0 @   Ƞ  X1*͠ƠibSߠΠ@H  k F l m Ko ʠ Ð@@@@9,mul_shuffle1 @ /   ܠ  " XQz+@)I   m     s      @@@@e,mul_shuffle2 @ [ J    N E} K2!WJ<@UJ 6    6  ,  @@@@,mul_shuffle3 @  s D 1 Ԡ w n  IBޠϠt[Jse@~K _     Ǡ F ?>@@@@%le_wd @   k X    8 1Ԡ͠pi q@@A&NZBase'NZOrder&NatInt'Numbers#Coq@@A@'NZOrder&NatInt'Numbers#Coq@+NZOrderProp)'@A@@@@"NZ@A@@ װ0  @@I@@AA@@A@*lt_le_incl @  ߠ   @  ڠ } v  QJ;ǠE8*@CA S .T@  + '@@@@@''le_refl @   Ԡ  d     = 6٠Ҡun_ڠi\N@gB w M ,@@Q@@I.lt_succ_diag_r @ 6 %    )  à  _ X& ~p@C   @@@@@l.le_succ_diag_r @ Y H    L C  ߠ  {  I0@D4 #@@@@@/neq_succ_diag_l @ { j ; ( ˠ n e     @ 9ܠՠƠkRAРà@EVީ TR@@"@@/neq_succ_diag_r @   ` M    - & ɠ   e ^ wf@F{ l@@@@@נ/nlt_succ_diag_l @ Ġ   q    Q J     %   @G' 㐩I@@@@@/nle_succ_diag_l @  נ   8 ۠ Ҡ u n     I B 3ؠ=0"@;HK#m@@@@@)le_succ_l @   ̠  \     5 . Ѡ ʠ m f WҠaTF@_IoJpϠH ;@@@@D+le_gt_cases @ 1   ޠ  $    Z S     | ! yk@J oem q@@@@i-lt_trichotomy @ V E    I @  ܠ  x      F - @K1'@@@@@(lt_asymm @ | k < ) ̠ o f     A : ݠ ֠ Ǡ l S BѠĠ@LW߶@}@@$@@(lt_trans @   b O    / ( ˠ Ġ g `     y h@M}.@ ڶ@O ܐ@@L@@ݠ(le_trans @ ʠ   w    W P     + $    @N-.V/@۶@ܩ'@@L@@+lt_strorder @  ߠ   @  ڠ } v     Q J ;  Ǡ E8*@CO<@+StrictOrder.[@ZC@@3@@++le_preorder @   ؠ Š h     A : ݠ ֠ y r c   ޠm`R@kPd@(PreOrder@W@@[@@S/le_partialorder @ @ /    3 * ͠ Ơ i b      0  z@Q@,PartialOrder5͛ ~@P$$H@@@E@A@@AhC@ABC@@)lt_compat @@/^@@@@@%lt_wd']ɠ  s D 1 Ԡ w n     I B  ޠ Ϡ t [ J٠̠@@@@@(lt_total @F@VG8@;/@]aǠ   n [    ; 4 נ Р s l      t@@@@@ࠠ'le_lteq @@.))@Y@+lt_eq_cases&y נ Ơ   ' ʠ  d ]     8 1 " Ǡ  ,@@@@@ 0Private_OrderTacjA'IsTotalr A: @=@:@(eq_equiv7L   ʠ  Z     3 , Ϡ Ƞ k d U   Р_RD@@@@@<9 @@A^π@&@F,Q^1   ޠ  $    Z S     | !  yk@@@@@cܐ @@z`@۠VE  I @  ܠ  x      F - @@@@@Ґ @@C@ Ѡ{j;( ˠ n e     @ 9 ܠ ՠ Ơ k R AРà@@@@@͐ @<@n@Ő̠`M    - & ɠ   e ^     w f@@@@@@@@@@#Tac6A  @Ƞu   U N     ) "    @@D!P)OrdersTac*Structures#Coq@+@@@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@'@$zero&CT@@A@ABCDE@A@G,MakeOrderTacBq?@A@@@BONR@@@A@@AEUH@@@N@!tJ@@A@A$:@@"eq$:^@@A@$@ @"le$h@@A@$@@"lt$ h@@A@ABC@A@+*OrderFacts.#@A@@s@X@@}@@AA@@A@Q @dS$WN     ) " Š   T ; *WPJ/@AV@@@@) @yJ7ڠ}t   O H   ՠ z a PߠҠĠ }vpU@B@@@@O \ @p]=6 ٠ Ҡ u n      vؠ{@C@ @@@@w*le_antisym @٠Ƞ)̠àf_    : 3 $ ɠ  .!̠Š@D"B C@@ ߩ$@@ @@  @ĠT-& ɠ   e ^ O  ۠ ʠYL><,@=EMmKn @@@@@ʠ*interp_ord @!o)OrdersTac@#ordȠ@ @@@@@@@@@@@Diua@ +k= R'6'6'6''+k+7T'+7T'6'ࠒA[kji@@"lt\ @@"eq8L@lР@4Ƞ@@10/@@A@B@A@xA܀ud5"Šh_:3 ֠ Ϡ  e L ;ʠha[@@@@@@8%trans @ZG' à_X     q `ԠҠ e@F"o'  @ ? @ VF/Wf@  @)trans_ord-0uG b@@ _@@{ G @ )* +!@O0aМA@56 7@ @ / L+k() LL7#'@f$tL%]VG  Ӡ  QD64$@@@@@W @MmKn oDМCD@UuSv wH L+k() NN7#'=t5$( ^W%  }om](!@@@@@ @ }М0B}@ & L+k() MM7#'vtn].aX3,ϠȠ^E4àaZT9@@@@@1+le_lt_trans @ Xs:6T@ ]@ߐ L+k() MN7#'tfS3,ϠȠkd}lޠΠq@@@@@i+lt_le_trans @ rn@ @@ L+k() NM7#'tߠΠ/Ҡɠle@9*Ϡ4'ҠˠŠ@@@@@%eq_lt @1Q/R S($%@6V4W X@ P L+k() ML7#'tנĠg @9ܠՠxqbݠl_QO? @@@@@ڠ%lt_eq @ig `\]@nl @@  L+k() LM7#'XtP?C:ݠ֠yr@'xC<6@@@@@%eq_le @·÷ :ĩU6@Ƕȶ ?ɶ@ = L+k() NL7#'twH5ؠ{rMFӠx_NݠР {tnS@@@@@K%le_eq @ rPn@ w@@ vҐ L+k() LN7#'ɐtnNG"  @@@@@&eq_neq @ՠ6٠РslG@1֠;. ٠Ҡ̠@G/O-P Q@ Ŷ@ ȩ@@@@@&neq_eq @ՠ e>7ڠӠvo`۠j]OM=@NH^~\ @.@ -@@@@@ޠ*not_neq_eq @@/3*͠Ơib0zxh3,& @yI@gK @@ @@ )not_ge_lt @kZ+^U0)̠Š[B1^WQ6@JԶն@А@@@@4)not_gt_le @VC#[Tm\ޠРΠ|a@K@l@@@@@_)le_neq_lt @nNG"   @L *+@@ک @@@@@@@@@Ր@@@@@א@<_neq @ߠ@ڠ}vQJ;Ǡ E 8 *@ CRS.T@@@@@@ &&le_neq @Ӡc<5ؠѠtm^٠ h [ M@ fSvQw֠A@#andЖw@W@@@@@ R*eq_le_incl @?.2)̠Šha/   y@ T}@k O@@@@@ u(lt_stepl @bQ"UL' àR9(   @ UŶƶ=Ƕ@@:8@@@@@ (lt_stepr @wH5ؠ{rMFӠx_N ݠ Р @ V]@@@@@ (le_stepl @hU5.Ѡʠmf n   @ W   @ @~@@@@@ ᠠ(le_stepr @Π{[T/( #  @ !X2@@@@@ [ @ܠ=נzsNG8ݠĠ B 5 '@ @YP+Q yRk@@@@@ #E @Ϡ_81Ԡ͠piZՠ d W I@ bZrMs tU@@@@@ E+le_antisymm @2!ߠ%[T}"   z l@ [ pS@@@@@ g)le_succ_r @TCG>ڠ}vD+   @ \/`c@@@@@ )lt_succ_l @|k<)̠of A:ݠ֠ǠlSB Ѡ Ġ @ ]W߶@ڐ@@@@@ ,le_le_succ_r @`M-&ɠ e^wf   @ ^{@۩۠@@@@@@ ؠ,lt_lt_succ_r @ŠrRK&   @ _()@%@@@@@ ,succ_lt_mono @ؠ9ܠӠvo JC4٠ > 1 #@ <`L'M9@@@@@ !,succ_le_mono @Π^70Ӡ̠ohYԠ c V H@ aaqLrѠJJ@@@@@ F<_0_1 @3"&\U~#   { m@ b@@@@ h&le_0_1 @UDH?۠~wE,   @ c"@@@@@ <_1_2 @ve6#Ơi`;4נРfM< ˠ  @ d @@@@ <_0_2 @XE%]Vo^   @ eL@@@@ ͠&le_0_2 @zg G@ܠx   @ f"@@@@@ <_1_l @۠ʠ+ΠŠha<5&ˠ 0 # @ .g>?@*@ ;-h@@@@@ @ABC@@ +lt_ge_cases @ƠV/(ˠĠg`Qݠ̠ [ N @@ YhiDj:4F@@@@@ =+le_ge_cases @*נzSLu  r d@ }ih^fj@@@@@ a+lt_gt_cases @N=A8۠Ԡwp >%   @ j)R~ @@@@@ ,eq_decidable @tc4!Ġg^92ՠΠdK: ɠ  @ kO׶ة)Decidable9@)decidable r@@@@@ &eq_dne @`M-&ɠ e^wf   @ l{c[͐@@@@@ נ&le_ngt @ĠqQJ%   @ m'()@@@@@ &nlt_ge @נ8۠Ҡun IB3ؠ = 0 "@ ;nK&L *@@@@@ !,lt_decidable @Π^70Ӡ̠ohYԠ c V H@ aoqLr$@@@@@ D<_dne @1 ޠ$ZS|!  y k@ p oSKa@@@@@ j&nle_gt @WFJAݠyG.   @ q2y (@@@@@ <_nge @}l=*͠pg B;ޠנȠmTC Ҡ Š @ rX@ @@@@@ ,le_decidable @aN.'ʠàf_xg   @ s|-H@@@@@ נ&le_dne @ĠqQJ%  @t'(o@@@@@ *nlt_succ_r @٠:ݠԠwp KD5ڠ?2$@=uM(N <@@@@@%5lt_exists_pred_strong @Ҡb;4נРsl]ؠgZL@evuvQw@b@@ 5@"ex @!k e_F@@@!@A@@Ag@AРD.Morphisms_Propy@A1@D@ABCD@@j.lt_exists_pred @WFJAݠyG.@w03@B<F5@@@/@A@@,lt_succ_pred @rC0Ӡvm HAݠΠsZIؠˠ@x\_@Ơs%?@@@@A-@\@@\@ABCD@@à&rs_rs' @p]=6٠Ҡun v@yx v@ٶ@@@T!@_@%&@ @ GK dH@@A@@(rs'_rs'' @۠<ߠ֠yrMF7ܠàA4&@?zEQ@S@*@W2X@/˶@ yI?@` ԩא@@@@5%rbase @"Ϡr KD|mwj\@u{{c@q@ -@@@@@\)A'A_right @I8 <3֠Ϡrk9 @|#@')@@ ѩ &.@@@@@@6strong_right_induction @ve6#Ơi`;4נРfM<ˠ@}>϶<Q۶@Uݶ@Ð@@@t@AL@@R@ABC@@/right_induction @`M-&ɠ e^wf@~hf{@ɶ@@F B@@@@@۠0right_induction' @ȠuUN)"@!-@/@ y@@@ @@7strong_right_induction' @ޠ?٠|uPI:ߠƠD7)@B@HT@'@W@?@[6\@Զ@{JA@@@@@1&ls_ls' @ ޠˠnG@ܠxisfX@qAwI@G@@q{@E׶@cֶ@ m@j x@Bm k@@R@@h(ls'_ls'' @UDH?۠~wE,@B0@4@@8@4@pi;g>Ʃ% : =@@@@%lbase @wH5ؠ{rMFӠx_NݠР@CPb쩷f@@e@@@@@à(A'A_left @p]=6٠Ҡun v@Dx @@@g@-f@@@@5strong_left_induction @۠ʠ+ΠŠha<5&ˠ0#@.E4@@B@S(@@@@@@ABC@@.left_induction @ĠT-&ɠ e^O۠ʠYL>@WF]/ʶi@-@l@d@@@@@>/left_induction' @+ؠ{TMvse@~GV@ @iܶ@Q@@O@@e6strong_left_induction' @RAE<ߠؠ{tB)@H}-@'@2@˶@6@2}@ne9@@~@@/order_induction @pA.ѠtkF?̠۠qXG֠ɠ@IIڶG\@@Ѷ@b@^@ d¶g a@@@@0@AB@@à0order_induction' @p]=6٠Ҡun v@Jx v @ٶ@@ @@0@@.@@1order_induction_0 @ܠˠ,ϠƠib=6'̠1$@/K 5@@ C@@*@ I@4r@@@@@2order_induction'_0 @ ɠY2+ΠǠjcTϠ^QC@\L b4϶@@-@ q@H@Y WY2@@@@@F<_ind @3"&\U~# {m@M ^  @j @v @%x @@@@@@q&le_ind @^M QH#N5$@N &  $ ; ö@@  @@@@@&Rlt_wd @tE2ՠxo JCߠРu\Kڠ͠@O^   շ c   s@@@@&Rgt_wd @lY92ՠΠqj r@P! ! !! ~ А@@/@@栠%lt_wf @Ӡ #Ơ`Y4-à( @&Q!6"Wf @,well_founded8E!@V@@@!\A𱍠G@!`A7iA@AB@@%gt_wf @ƠV/(ˠĠg`Qݠ̠[N@@YR!i3!kZ@@+@@<-add_lt_mono_l @)֠yRKt@@!! d!!  w@@@@AA@@A@-add_lt_mono_r @O>B9ܠՠxq ?&@A!'! !!! }@@@@&+add_lt_mono @ra2 e\70Ӡ̠bI8@4B!J!Ҷ !Ӷ!ԶJ!ն@ @ϩ  R!" Tѐ@@@@@N-add_le_mono_l @ZG' à_Xq`@\C!r! !#!![ @@@@q-add_le_mono_r @}j JCߠ{@D!" "F"!~̩ @@<@@+add_le_mono @Ϡ0Ӡʠmf A:+Р@E!"@!"Ai"B"C@!@!o@@@@@.add_lt_le_mono @ŠU.'ʠàf_Pܠ@F!"e!@"f"g"h@ <@@@@@@ܠ.add_le_lt_mono @(ՠxQJs@G""!c"""@H@@@@@+add_pos_pos @J9 =4נРsl:!@ H"""!"@l@m!!@@j@@!.add_pos_nonneg @m\-`W2+ΠǠ]D3@/I"E"Ͷ!"ζ@@!$@@@@C.add_nonneg_pos @~O<ߠyTMڠfU@QJ"g"!"@!E@@@@c1add_nonneg_nonneg @o\<5ؠѠtm u@qK"#!#@A@B!e@@@@,lt_add_pos_l @Ѡ~!Ġ^W2+@L"#1" #2@""T@@@"@#@AB@@,lt_add_pos_r @Eߠ{VO@̠@M"#U"0#V@ "A"!@@@@̠,le_lt_add_lt @  ؠŠh A:ݠ֠yrc@N"#x"S#y#z#{@8@"g!!"" U@@@@@,lt_le_add_lt @ @ / 3*͠Ơib0@O##"{###@ w@"{( y@@@@@,le_le_add_le @ d S $ WN)"ŠT;*@&P#<#Ķ"#Ŷ#ƶ<#Ƕ@@$@@@@@;,add_lt_cases @  v G 4נzq LEҠw^M@IQ#_#"##_#@"\""_@@@@@a,add_le_cases @   m Z:3֠Ϡrks@oR#$ "$6$$@"""@@@@@-add_neg_cases @ Ӡ     #Ơ`Y4-à@S#$3#$4@#"l####" ##%##@@}@@-add_pos_cases @     K$\UFҠ@T#$[#6$\@#G#"#/#K#"3 #@@ @@ՠ0add_nonpos_cases @!!!  Π q  JCߠ{l@U#$#\$@#YN#T#\M#]L@@@@0add_nonneg_cases @!F!5!   9 0Ӡ̠oh 6 @V$$#$@#~K#y#Jܐ@@ g@@-le_exists_sub @!j!Y!*!  ] T/(ˠĠZA0@,W$B$ʶ#$˶@#R$η$ϩ V$"#LF@@@$j@AB@$@A$AAH@F@@ABCD@@O+mul_lt_pred @!!![!H    ( !Ġ`Y@@ $o$$s$#$@$۠$$H"ѩ$`##`#a$K$Z##s$^#r"ސ@@(@@AA@@A@1mul_lt_mono_pos_l @!Ϡ!!!|!    \ U0)@AT%-$%.$ %/@ϩ$*$@@@$@At@@%@@ABCD@@+1mul_lt_mono_pos_r @!!!!!G    }  XQB@?B|%U$%V$1%W@$R$D#˩#$$@@y@@Q1mul_lt_mono_neg_l @"" !ݠ!ʠ!m!!   F ?۠~wh @eC%{$%|$W%}@E$ݠx$j@@N@@t1mul_lt_mono_neg_r @"@"/"!!!3!* ͠ Ơ i b 0@D%%%$z%@h%$HI@@@@4mul_le_mono_nonneg_l @"c"R"#"!!V!M     ( !ĠS@E%9%$%¶%ö@@$$"#% m@@ @@4mul_le_mono_nonpos_l @""v"G"4!נ!z!q!!    L EҠw@F%]%$%%@v@$$@@+@@ݠ4mul_le_mono_nonneg_r @"""i"V!!!!6!/ Ҡ ˠ n g  @G%&$&0& @ƶ@ǩ$t@@M@@4mul_le_mono_nonpos_r @"ˠ"""x"!!!X!Q     , % @ H%&)%&*R&+@@%*@@o@@!,mul_cancel_l @""ܠ"""=!!נ!z!s!!   N G 8@ 5I%&K%&&Lt&M@% &.$x%&1$@@@%@&0@m@ABC@@K,mul_cancel_r @##"נ"Ġ"g" "!!!@!9 ܠ ՠ x q b @ _J%&u%P&v&w@*%נ&X6@@@@n(mul_id_l @#:#)""""-"$!Ǡ!!c!\      *@ K&&%s&@L%&z%&|$p%Ð@@ @@(mul_id_r @#^#M## ""Q"H!!!!!#!    N@ L&4&%&@%z&& &$&&%@@@@1mul_le_mono_pos_l @##t#E#2"ՠ"x"o"" !!!J!C  ߠ Р u@ M&[&%& &@%%0&F%@@*@@ܠ1mul_le_mono_pos_r @###h#U""""5".!Ѡ!ʠ!m!f! !  @ N&~'%'/'@#&hǩ%@@&@@1mul_le_mono_neg_l @#ʠ###w#"""W"P!!!!!+!$! @!O&'(&')Q'*@&&Ґ@@ @@!1mul_le_mono_neg_r @##ܠ###=""נ"z"s""!!!N!G!8 @!5P&'K&&'Lt'M@& &&z@@l@@D2mul_lt_mono_nonneg @$##Р##`#""""9"2!ՠ!Π!q!j![!@!XQ&'n&I'o'p'q@&H&&@&_&&@@&c%֠ P8%ؠa&@@@@@q2mul_le_mono_nonneg @$=$,####0#'"ʠ"à"f"_"!!!!!-@!R''&v'''@-@&v+@0@&y*@@@@+mul_pos_pos @$b$Q$"$##U#L"""""'" !à!!!R@!S'8'&'@ @ &',@@ @@+mul_neg_neg @$$r$C$0#Ӡ#v#m## """H"A!!ݠ!Π!s@!T'Y'&'@@!@@ @@֠+mul_pos_neg @$$$b$O####/#("ˠ"Ġ"g"`"!!!@!U'x(&(@ ¶@ȩ&l'U@@E@@+mul_neg_pos @$à$$$p$###P#I"""""$""!@" V'(!&("@@ !@@ @@1mul_nonneg_nonneg @$$Ѡ$$$2#ՠ#̠#o#h# #"""C"<"-!@"*W'(@'(A@r@s'@@ @@60mul_pos_cancel_l @%$$ $$R#####+#$"Ǡ""c"\"M!@"JX'(`';(a@"''N'&@@1@@X0mul_pos_cancel_r @%$%$$Ѡ$t$$###M#F""""~"o"@"lY'('](@'"%@@Q@@x3mul_nonneg_cancel_l @%D%3%$$$7$.#Ѡ#ʠ#m#f# #""""4@"Z(('}(@d('|Bא@@r@@3mul_nonneg_cancel_r 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@'p'_'0'&&c&Z%%%%%5%.$Ѡ$ʠ$$`@$g*F*ζ)*϶@)))K))/)()1)**@@ @@ʠ*add_le_mul @'''V'C&&&&#&%%%[%T$$$$@$h!a*!b*@@)Ѡld@@"=@@-square_nonneg @'''{'h' &&&H&A%%ݠ%%y%%%$@%i%+)*kː@@@@ 5crossmul_le_addsquare @'٠'Ƞ''')&̠&à&f&_&%%%%:%3%$$@%!jC+7A+8@i@j*))@@R@@1-add_square_le @'''''M&&&&&&&% %%^%W%H$@%Ekg+[e+\@@*4")ѐ@@"@@T-square_add_le @( (''͠'p'' &&&I&B%%ޠ%%z%k%@%hl+~+@@*W#)ޠ*G@@"@@w4quadmul_le_squareadd @(C(2('''6'-&Р&ɠ&l&e&&%%%%3@%m++@Ӷ@ԩ*z******)|L@@"@@(pred_inj @(j(Y(*('']'T&&&&&/&(%@&%@+=+Ŷ*+ƶ@+)Q#<@@# @@AA@@A@+pred_inj_wd @((y(J(7'ڠ'}'t''&&&O&H%@&EA#-+#+++E!*@@"@@'succ_m1 @(((f(S''''3',&Ϡ&Ƞ&k&d&@&aB+ޠ+)t++U@@"@@<*add_pred_l @(à(((p('''P'I&&&@&@+,*,+*5++*X@@"<@@AA@@A@*add_pred_r @((Ҡ(((3'֠'͠'p'i' '&@'A+,<+,=,*+) @@"[@@)add_opp_r @(((((O'''''('!&@'B+,X+3,Y,7*Ԡ+)*s@@"w@@;'sub_0_l @)) (۠(Ƞ(k(('''D'=&@':C+,t,R**)ǐ@@"@@U*sub_succ_l @)5)$((((((' ''^'W&@'TD,,+i,,m**̩,,*@@"@@q*sub_pred_l @)Q)@)(((D(;'ޠ'נ'z's'@'pE,",+,,+*Ɛ@@"@@*sub_pred_r @)l)[),)((_(V'''''1@'F,=,Ŷ+,Ʃ,+27@@"@@(opp_pred @))v)G)4(נ(z(q(( '''L@'G,X,,*R*l,}*5@@$Q@@ (sub_diag @)))b)O((((/(('ˠ'Ġ'g@'H,s,,٠+g+,N@@#@@ܠ.add_opp_diag_l @)))|)i) (((I(B''ޠ'@'I,-,+*i,,i@@#3@@.add_opp_diag_r @)נ)Ơ)))'(ʠ((d(](''@'J,-0-+,*,@@#N@@)add_opp_l @)))))B((ܠ((x(('@(K,-K,&-L-*+Ǡ*,+f@@#j@@.-add_sub_assoc @*))Π))^)((((7(0'@(-L,-g,B-h"-i-G++=++"@@#@@L.opp_involutive @*,*))٠)|))(((U(N'@(KM,--c**,@@#@@f-opp_add_distr @*F*5*)))9)0(Ӡ(̠(o(h( @(eN--,z--~++٩,++*@@#@@-opp_sub_distr @*d*S*$*))W)N((((()@(O-5-,--+0+ة,:-3@@#@@'opp_inj @**p*A*.)Ѡ)t)k))(((F@(P-R-ڶ,-۶@-9%P@@%@@*opp_inj_wd @***[*H))))()!(Ġ((`@(Q-l-,--T,@@% @@ՠ(eq_opp_l @***u*b*)))B);(ޠ(נ(z@(R-.,.-n-P-@@$-@@(eq_opp_r @*Ѡ***~*!)Ġ))^)W(((@(S-.*-.+-@@@@@ -sub_add_distr @**ڠ***;)ޠ)ՠ)x)q)) (@) T-.D-.E#m.F.$,#k,,,-@@$f@@*-sub_sub_distr @+ **ʠ**Z)))))3),(@))U-.c->.d#.e.C,,@@$@@G)sub_opp_l @+'+**Ԡ*w**)))P)I(@)FV-.-[.._,©,6@@$@@c)sub_opp_r @+C+2+***6*-)Р)ɠ)l)e)@)bW..-w..{- D,Ր@@$@@~,add_sub_swap @+^+M++ **Q*H)))))#@)}X./.-.#..N-4-'#.@@$@@,sub_cancel_l @+|+k+<+)*̠*o*f* *)))A@)Y.M.ն-.ֶ#.ש.6.-@@$@@,sub_cancel_r @+++Y+F****&*) ))^@)Z.j.-.$..S.Ԡ;-&k@@%@@֠*add_move_l @+++v+c+***C*<)ߠ)ؠ){@)[./-/$8/.p.$4..h-$ @@%1@@*add_move_r @+ՠ+Ġ+++%*Ƞ**b*[)))@)\./.. //$W/0./---@@%O@@*sub_move_l @+++++C**ݠ**y**)@*]./L.'/M$u/N././/=@@%m@@1*sub_move_r @,,+Ѡ++a+****:*3)@*0^./j.E/k$/l.ˠ/L-@%@@%@@N,add_move_0_l @,.,++۠+~+!+***W*P)@*M_./.b/.砩/h U/i.@@&@@k,add_move_0_r @,K,:, +++>+5*ؠ*Ѡ*t*m*@*j`//.//@@'@@,sub_move_0_l @,e,T,%,++X+O******@*a/6/.///-//- @@'2@@,sub_move_0_r @,,r,C,0+Ӡ+v+m++ ***H@*b/T/ܶ./ݩ/<.@@'L@@+add_simpl_l @,,,],J++++*+#*Ơ**b@*c/n/.//ՠ.c.0/M/k@@&@@٠+add_simpl_r @,,,y,f, +++F+?**۠*~@*d/0.0/..L//i@@&1@@+sub_simpl_l @,ՠ,Ġ,,,%+Ƞ++b+[***@*e/0./ 0/0 ./-@@&M@@+sub_simpl_r @,,,,,A++۠+~+w++*@+f/0J/%0K0).Ơ.e//@@&i@@-'sub_add @- ,,͠,,],++++6+/*@+,g/0f/A0g0E.7//ې@@&@@I1add_add_simpl_l_l @-)-,,֠,y,,+++R+K*@+Hh/0/]0%00b.%%P.@@&@@f1add_add_simpl_l_r @-F-5-,,,9,0+Ӡ+̠+o+h+ @+ei00/z0%00/ %%.@@&@@1add_add_simpl_r_l @-c-R-#-,,V,M+++++(@+j040/0%00/*%.@@&@@1add_add_simpl_r_r @--o-@--,Р,s,j, ,+++E@+k0Q0ٶ/0ڶ&0۩0/G%&}"@@&@@1sub_add_simpl_r_l @---]-J,,,,*,#+Ơ++b@+l0n0/0&00֠/s/1%Đ@@'@@ڠ1sub_add_simpl_r_r @---z-g- ,,,G,@++ܠ+@+m01/1&<10/&%@@'3@@*mul_pred_r @-נ-Ơ---',ʠ,,d,],@,Z@01.0 1/1 //$Ґ@@'M@@AA@@A@*mul_pred_l @-----D,,ޠ,,z,@,wA01K0&1L1*////I@@'j@@)mul_opp_l @.--Π--^-,,,,7@,B01e0@1f1D/.ِ/c@@'@@8)mul_opp_r @.).--֠-y--,,,R@,C010[11_/(@@'@@Q+mul_opp_opp @.B.1.---5-,,Ϡ,Ƞ,k@,D110t11x//@@'@@j,mul_opp_comm @.[.J..--N-E,,,@,E1*1011M2@@'@@/mul_sub_distr_l @.s.b.3. -à-f-]-,,@,F1B1ʶ01˶&1̩10)c09$@@'@@/mul_sub_distr_r @..}.N.;-ޠ--x--,@-G1]101'11Š0D0T%=@@(@@-neg_pos_cases @...i.V----6@-@1v11] 0Р @@@@@AA@@A@0nonpos_pos_cases @.à...p.---P@-A120 4@@@@@0neg_nonneg_cases @.ؠ.Ǡ...(-ˠ- -e@-B12-0@@@@@-3nonpos_nonneg_cases @..ܠ...=--נ-z@-C12B1@@@@@B)lt_pred_l @/.. ..R---@-D12W1A/1ɐ@@)@@W)le_pred_l @//.נ.Ġ.g. .-@-E12l1B@@@@@k*lt_le_pred @/+/..ؠ.{..-@.F121[211K1YD@@(@@*nle_pred_r @/B/1/...5.,-@.)G221S1o2 0#@@@@@*lt_pred_le @/Y/H//..L.C-@.@H2&212211@@}@@*lt_lt_pred @/p/_/0/..c.Z-@.WI2=2Ŷ12ƶ@112@@@@@Ǡ*le_le_pred @//v/G/4.נ.z.q.@.nJ2T2ܶ12ݶ@11@@@@@ݠ*lt_pred_lt @///]/J....*@.K2j212@1"@@@@@*le_pred_lt @///s/`/...@@.L2313 @$@@@@@,pred_lt_mono @/Ƞ///u/...U@.M23132}12 Y@@@@@,pred_le_mono @/ߠ/Π////.Ҡ.ɠ.l@.N23423522 2 p@@@@@6/lt_succ_lt_pred @/////F...@.O23K2&3L2mZ@@@@L/le_succ_le_pred @0 //̠//\...@.P23a2<3b2#@@/@@b/lt_pred_lt_succ @0"0//Ϡ/r// .@/ Q23w2R3x2נ2 @@@@@x/le_pred_lt_succ @080'////+/".@/R332h322fqא@@)@@*neq_pred_l @0O0>0///B/9.@/6S332`3O@@@@@'lt_m1_r @0e0T0%0//X/O.@/LT32323@2@23@@@3U@A*@+/@A3@3A1ՠF-SetoidTactics3@3A1I@ABCD@@ˠ+add_neg_neg @00z0K08/۠/~@/@3V3޶23߶@@2ˠ(R33@@+#@@AA@@A@.add_neg_nonpos @000d0Q//@/A3o323@@s@@+:@@.add_nonpos_neg @000x0e0/@0B34 24 @-@@+M@@*1add_nonpos_nonpos @0ˠ000x0/@0C3424@@2@@@+b@@?(lt_0_sub @00Ϡ0000/@0-D34334433 33@@*R@@U(le_0_sub @00000F/@0CE34I3$4J33"3#@@*g@@j(lt_sub_0 @1 00ˠ00[/@0XF34^394_33K3*@@*|@@(le_sub_0 @1 100͠0p0@0mG34s3N4t3Ӡ3L3M@@*@@+opp_lt_mono @151$0000(@0H443c433S3uȐ@@*@@+opp_le_mono @1J191 000=@0I443x433v3vݐ@@*@@+opp_pos_neg @1_1N11 00R@0J4*44342l@@@@Ӡ+opp_neg_pos @1t1c141!0Ġ0g@0K4?4ǩ4&324 @@*@@蠠1opp_nonneg_nonpos @11x1I160٠0|@0L4T4ܩ4;3*m@@@@1opp_nonpos_nonneg @111]1J00@0M4h44O3)@@+ @@'lt_m1_0 @111q1^10@0N3 4U@@@@@"-sub_lt_mono_l @1à111p10@1O4535*?54w%4@@+6@@9-sub_lt_mono_r @1ڠ1ɠ111*0@1'P45-45.*V5/4%)4;@@+L@@O+sub_lt_mono @11ߠ111@0@1=Q45C45D*l5E)5F@@%e423q3%A@@@@@i-sub_le_mono_l @2 11ʠ11Z0@1WR45]485^*5_4' 47G@@+|@@-sub_le_mono_r @2 211͠1p1@1mS45s4N5t*5u4Ԡ'"4M@@+@@+sub_le_mono @262%1111)@1T554d5*5*5@I@"I4dF@@@@@.sub_lt_le_mono @2M2<2 111@@1U554{5*5*5@w@"`]@@@@@ .sub_le_lt_mono @2c2R2#211V@1V5.545*5*.5@vs@@@@@נ,le_lt_sub_lt @2x2g282%1Ƞ1k@1W5C5˶45̶*5Ͷ*C5ζ@@44< 4=v@@-@@,lt_le_sub_lt @222R2?11@1X5]545+5*]5@@4@@-+@@,le_le_sub_lt @222i2V11@1Y5t545+%5*t5@@@@-A@@/lt_add_lt_sub_r @2222l21@2 Z5646+;65s5*5@@@@5/le_add_le_sub_r @2֠2Š222&1@2#[56)56*+R6+55*˩5Ð@@@@L/lt_add_lt_sub_l @22ܠ222=1@2:\56@56A+i6B5.5.54-@@@@d/le_add_le_sub_l @322Š22U1@2R]56X536Y+6Z5/52@@(@@z/lt_sub_lt_add_r @33 2۠2Ƞ2k2@2h^56n5I6o+6p5Ϡ5\5]+@@?@@/le_sub_le_add_r @323!22ߠ22%@2_565`6+65栩5_Ω5`+@@V@@/lt_sub_lt_add_l @3I383 222<@2`665w6+655W.@@,@@/le_sub_le_add_l @3_3N33 22R@2a6*656+665m-@@,@@Ԡ-lt_sub_lt_add @3u3d353"2Š2h@2b6@6ȶ56ɶ+6ʶ+@6˩6*559+>45+@@,@@-le_sub_le_add @33~3O3<2ߠ2@2c6Z656, 6+Z66D55+)@@-@@*lt_sub_pos @333g3T22@2d6r6566Z556Q@@-@@-le_sub_nonneg @333}3j3 2@3 e67576pϩ5@@-.@@1,sub_lt_cases @3Ҡ3333"2@3f67%67&,N7'+7(@\5'H@@@@@H,sub_le_cases @33ؠ33392@36g67<67=,e7>+7?@Y6#@@@@@_-sub_neg_cases @43333P2@3Mh67S6.7T@6%@@@@t-sub_pos_cases @443ՠ3 3e3@3bi67h6C7i@6T656< 3@@.@@0sub_nonpos_cases @4,433٠3|3@3yj676Z7@ 6Q@@>@@0sub_nonneg_cases @4A4043334@3k7 76o7@6l,6g@@.@@,zero_pos_neg @4W4F4433J@3l!P7$P_wd7@7@7*7@ͩ :6 6@@@@Ԡ2mul_lt_mono_nonpos @4u4d454"@4@7>7ƶ67Ƕ,7ȶ,>7ɶ@D@V@F@X6RT@@@@@AA@@A@2mul_le_mono_nonpos @444P4=@49A7Y767- 7,Y7@_@F@a@H6@@@@@1mul_nonpos_nonpos @444g4T@4PB7p767@s@t@@@@,1mul_nonneg_nonpos @444y4f@4bC78 68 @<@6 @@/N@@?1mul_nonpos_nonneg @4̠444y@4uD7868@@P@@@@Q(lt_mul_0 @4ޠ4͠44@4E78/7 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