Welcome to Coq V6.2.2 (September 1998) No .coqrc or .coqrc.6.2.2 found. Skipping rcfile loading. [Loading ML file xml.cmo ...done] [Loading ML file xmlprinter.cmo ...done] [Loading ML file xmltest.cmo ...done] [Loading ML file test.cmo ...done] Grammar Marker #_13.obj : Unrecognized object ML-MODULE #_12.obj : Unrecognized object ML-MODULE #_11.obj : Unrecognized object ML-MODULE #_10.obj : Unrecognized object ML-MODULE >>>>>>> Import Prolog >>>>>>> Import Program >>>>>>> Import Tauto >>>>>>> Import Inv >>>>>>> Import Equality >>>>>>> Import ProPre >>>>>>> Import Logic_TypeSyntax >>>>>>> Import Logic_Type >>>>>>> Import Prelude >>>>>>> Export IO
#Prolog#_0.obj : Unrecognized object ML-MODULE Grammar Marker Syntax Marker
#Program#_0.obj : Unrecognized object ML-MODULE Grammar Marker Grammar Marker Grammar Marker Grammar Marker Grammar Marker Grammar Marker Grammar Marker Syntax Marker Syntax Marker
#Tauto#_0.obj : Unrecognized object ML-MODULE Grammar Marker Syntax Marker
>>>>>>> Export Equality #Inv#_1.obj : Unrecognized object ML-MODULE Syntax Marker Grammar Marker Grammar Marker
#Equality#_0.obj : Unrecognized object ML-MODULE Grammar Marker Syntax Marker
#ProPre#_0.obj : Unrecognized object ML-MODULE Grammar Marker Grammar Marker Grammar Marker
>>>>>>> Import Logic_Type Grammar Marker Syntax Marker
>>>>>>> Export Logic >>>>>>> Import LogicSyntax #Logic_Type#allT.obj 4 AProp A P x #Logic_Type#allT.obj 4 AProp Prop
#universal_quantification#Logic_Type#A.obj 10 AProp A A P x0 H x A allT A A P x0 P x Prop A B P y B A f x H Prop A B P y B allT A P
Universes of #Logic_Type#universal_quantification#A.obj (6 uni,4 edges) Universes of #Logic_Type#universal_quantification#P.obj (6 uni,5 edges) #universal_quantification#Logic_Type#A.obj 10 AProp A allT A A P x0 P x #universal_quantification#Logic_Type#A.obj 10 AProp Prop A B P y B allT A P Inductive exT [A:#Logic_Type#exT.obj 11; P:AProp] : Prop := exT_intro : A P x exT A P #Logic_Type#exT.obj 11 AProp Prop A P x P0 exT A P "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x x0 exT_intro x x0 #Logic_Type#exT.obj 11 AProp Prop A P x P0 exT A P P0 Inductive exT2 [A:#Logic_Type#exT2.obj 31; P:AProp; Q:AProp] : Prop := exT_intro2 : A P x Q x exT2 A P Q #Logic_Type#exT2.obj 31 AProp Prop A P x Q x P0 exT2 A P Q "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x x0 x1 exT_intro2 x x0 x1 #Logic_Type#exT2.obj 31 AProp AProp Prop A P x Q x P0 exT2 A P Q P0 Inductive eqT [A:#Logic_Type#eqT.obj 59; x:A] : AProp := refl_eqT : eqT A x x #Logic_Type#eqT.obj 59 A AProp P x A eqT A x y "MULTCASE" P "TOMATCH" e "EQN" f refl_eqT #Logic_Type#eqT.obj 59 A AProp P x A eqT A x y P y Add Auto Marker
#Equality_is_a_congruence#Logic_Type#A.obj 76 #Equality_is_a_congruence#Logic_Type#B.obj 81 AB A A A eqT A x y eqT_ind A x A eqT A a x refl_eqT A x y H eqT A x y eqT A y x eqT A x y eqT A y z eqT_ind A y A eqT A x a H z H0 eqT A x y eqT A y z eqT A x z eqT A x y eqT_ind A x A eqT B f x f a refl_eqT B f x y H eqT A x y eqT B f x f y not eqT A x y eqT A y x H eqT_ind A y A eqT A a y refl_eqT A y x H' not eqT A x y not eqT A y x
Universes of #Logic_Type#Equality_is_a_congruence#A.obj (6 uni,4 edges) Universes of #Logic_Type#Equality_is_a_congruence#B.obj (6 uni,4 edges) Universes of #Logic_Type#Equality_is_a_congruence#f.obj (7 uni,5 edges) #Equality_is_a_congruence#Logic_Type#A.obj 76 A A eqT A x y eqT A y x #Equality_is_a_congruence#Logic_Type#A.obj 76 A A A eqT A x y eqT A y z eqT A x z #Equality_is_a_congruence#Logic_Type#A.obj 76 #Equality_is_a_congruence#Logic_Type#B.obj 81 AB A A eqT A x y eqT B f x f y #Equality_is_a_congruence#Logic_Type#A.obj 76 A A not eqT A x y not eqT A y x Add Auto Marker #Logic_Type#eqT_ind_r.obj 76 A AProp P x A eqT A y x "MULTCASE" A P a "TOMATCH" sym_eqT A y x H0 "EQN" H refl_eqT #Logic_Type#eqT_ind_r.obj 81 A AProp P x A eqT A y x P y Inductive EmptyT : #Logic_Type#EmptyT.obj 87 := EmptyTProp EmptyT "MULTCASE" P "TOMATCH" e EmptyTProp EmptyT P e EmptyTSet EmptyT "MULTCASE" P "TOMATCH" e EmptyTSet EmptyT P e EmptyT #Logic_Type#EmptyT_rect.obj 98 EmptyT "MULTCASE" P "TOMATCH" e EmptyT #Logic_Type#EmptyT_rect.obj 98 EmptyT P e Inductive UnitT : #Logic_Type#UnitT.obj 114 := IT : UnitT UnitTProp P IT UnitT "MULTCASE" "SYNTH" "TOMATCH" u "EQN" f IT UnitTProp P IT UnitT P u UnitTSet P IT UnitT "MULTCASE" "SYNTH" "TOMATCH" u "EQN" f IT UnitTSet P IT UnitT P u UnitT #Logic_Type#UnitT_rect.obj 125 P IT UnitT "MULTCASE" "SYNTH" "TOMATCH" u "EQN" f IT UnitT #Logic_Type#UnitT_rect.obj 125 P IT UnitT P u #Logic_Type#notT.obj 141 AEmptyT #Logic_Type#notT.obj 141 #Logic_Type#notT.obj 144 Inductive identityT [A:#Logic_Type#identityT.obj 155; a:A] : A #Logic_Type#identityT.obj 154 := refl_identityT : identityT A a a #Logic_Type#identityT.obj 155 A A identityT A a y Prop P a refl_identityT A a A identityT A a y "MULTCASE" P "TOMATCH" i "EQN" f refl_identityT #Logic_Type#identityT.obj 155 A A identityT A a y Prop P a refl_identityT A a A identityT A a y P y i #Logic_Type#identityT.obj 155 A A identityT A a y Set P a refl_identityT A a A identityT A a y "MULTCASE" P "TOMATCH" i "EQN" f refl_identityT #Logic_Type#identityT.obj 155 A A identityT A a y Set P a refl_identityT A a A identityT A a y P y i #Logic_Type#identityT.obj 155 A A identityT A a y #Logic_Type#identityT_rect.obj 204 P a refl_identityT A a A identityT A a y "MULTCASE" P "TOMATCH" i "EQN" f refl_identityT #Logic_Type#identityT.obj 155 A A identityT A a y #Logic_Type#identityT_rect.obj 204 P a refl_identityT A a A identityT A a y P y i Add Auto Marker
#IdentityT_is_a_congruence#Logic_Type#A.obj 241 #IdentityT_is_a_congruence#Logic_Type#B.obj 246 AB A A A identityT A x y identityT_rect A x A identityT A x y0 identityT A y0 x refl_identityT A x y X identityT A x y identityT A y x identityT A x y identityT A y z identityT_rect A y A identityT A y y0 identityT A x y0 X z X0 identityT A x y identityT A y z identityT A x z identityT A x y identityT_rect A x A identityT A x y0 identityT B f x f y0 refl_identityT B f x y X identityT A x y identityT B f x f y notT identityT A x y identityT A y x H identityT_rect A y A identityT A y y0 identityT A y0 y refl_identityT A y x H' notT identityT A x y notT identityT A y x
Universes of #Logic_Type#IdentityT_is_a_congruence#A.obj (6 uni,4 edges) Universes of #Logic_Type#IdentityT_is_a_congruence#B.obj (6 uni,4 edges) Universes of #Logic_Type#IdentityT_is_a_congruence#f.obj (7 uni,5 edges) #IdentityT_is_a_congruence#Logic_Type#A.obj 241 A A identityT A x y identityT A y x #IdentityT_is_a_congruence#Logic_Type#A.obj 241 A A A identityT A x y identityT A y z identityT A x z #IdentityT_is_a_congruence#Logic_Type#A.obj 241 #IdentityT_is_a_congruence#Logic_Type#B.obj 246 AB A A identityT A x y identityT B f x f y #IdentityT_is_a_congruence#Logic_Type#A.obj 241 A A notT identityT A x y notT identityT A y x #Logic_Type#identityT_ind_r.obj 261 A AProp P x A identityT A y x "MULTCASE" A identityT A x y0 P y0 "TOMATCH" sym_idT A y x H0 "EQN" H refl_identityT #Logic_Type#identityT_ind_r.obj 267 A AProp P a A identityT A y a P y #Logic_Type#identityT_rec_r.obj 272 A ASet P x A identityT A y x "MULTCASE" A identityT A x y0 P y0 "TOMATCH" sym_idT A y x H0 "EQN" H refl_identityT #Logic_Type#identityT_rec_r.obj 278 A ASet P a A identityT A y a P y #Logic_Type#identityT_rect_r.obj 287 A A #Logic_Type#identityT_rect_r.obj 290 P x A identityT A y x "MULTCASE" A identityT A x y0 P y0 "TOMATCH" sym_idT A y x H0 "EQN" H refl_identityT #Logic_Type#identityT_rect_r.obj 300 A A #Logic_Type#identityT_rect_r.obj 303 P a A identityT A y a P y Add Auto Marker Syntax Macro AllT = allT "ISEVAR" Syntax Macro ExT = exT "ISEVAR" Syntax Macro ExT2 = exT2 "ISEVAR"
>>>>>>> Export Core >>>>>>> Export Datatypes >>>>>>> Export DatatypesSyntax >>>>>>> Export Logic >>>>>>> Export LogicSyntax >>>>>>> Export Specif >>>>>>> Export SpecifSyntax >>>>>>> Export Peano >>>>>>> Export Wf
>>>>>>> Export Logic
Set A AProp Inductive Acc : AProp := Acc_intro : A A R y x Acc y Acc x AProp A A R y x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y A R y x P y P x F F A a #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) a a0 P a "MULTCASE" P "TOMATCH" a0 "EQN" f x a1 A R y x F y a1 y r Acc_intro x a1 AProp A A R y x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y A R y x P y P x A #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) a P a A #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) x "MULTCASE" A A R y a #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y "TOMATCH" H "EQN" H0 Acc_intro x0 H0 A #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) x A R y x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y
ASet A A R y x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y A R y x P y P x Acc_rec Acc_rec A x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) x a P x F x #GENTERM (CONST #Well_founded#Wf#Acc_inv.cci R A) x a A R y x Acc_rec y #GENTERM (CONST #Well_founded#Wf#Acc_inv.cci R A) x a y h A #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) x P x
ASet A A R y x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y A R y x P y P x Acc_rec Acc_rec A x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) x a P x F x #GENTERM (CONST #Well_founded#Wf#Acc_inv.cci R A) x a A R y x Acc_rec y #GENTERM (CONST #Well_founded#Wf#Acc_inv.cci R A) x a y h ASet A A R y x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y A R y x P y P x A #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) x P x A #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) a Prop #GENTERM (CONST #Well_founded#Wf#well_founded.cci R A) ASet A A R y x P y P x A #GENTERM (CONST #Well_founded#Wf#Acc_rec.cci R A) P A A R y x #GENTERM (MUTIND #Well_founded#Wf#Acc.cci 0 R A) y A R y x P y H0 x H2 a H a #GENTERM (CONST #Well_founded#Wf#well_founded.cci R A) ASet A A R y x P y P x A P a
Inductive Acc [A:Set; R: A AProp ] : AProp := Acc_intro : A A R y x Acc A R y Acc A R x Set A AProp AProp A A R y x Acc A R y A R y x P y P x F F A a Acc A R a a0 P a "MULTCASE" P "TOMATCH" a0 "EQN" f x a1 A R y x F y a1 y r Acc_intro x a1 Set A AProp AProp A A R y x Acc A R y A R y x P y P x A Acc A R a P a Set A AProp A Acc A R x "MULTCASE" A A R y a Acc A R y "TOMATCH" H "EQN" H0 Acc_intro x0 H0 Set A AProp A Acc A R x A R y x Acc A R y Set A AProp ASet A A R y x Acc A R y A R y x P y P x Acc_rec Acc_rec A x Acc A R x a P x F x Acc_inv A R x a A R y x Acc_rec y Acc_inv A R x a y h Set A AProp ASet A A R y x Acc A R y A R y x P y P x A Acc A R x P x Set A AProp A Acc A R a Set A AProp Prop Set A AProp well_founded A R ASet A A R y x P y P x A P a
Set A AProp well_founded A R AProp A A R y x P y P x A Acc_ind A R P A A R y x Acc A R y A R y x P y H0 x H2 a H a well_founded A R AProp A A R y x P y P x A P a
Set A AProp well_founded A R AProp A A R y x P y P x A P a
>>>>>>> Export Logic >>>>>>> Export LogicSyntax nat eq nat n m f_equal nat nat S n m H nat nat eq nat n m eq nat S n S m Add Auto Marker nat "MULTCASE" "SYNTH" "TOMATCH" n "EQN" O O "EQN" u S u natnat nat refl_equal nat pred S m nat eq nat m pred S m nat eq nat S n S m f_equal nat nat pred S n S m H nat nat eq nat S n S m eq nat n m Add Auto Marker nat not eq nat n m eq nat S n S m H eq_add_S n m H0 nat nat not eq nat n m not eq nat S n S m Add Auto Marker nat "MULTCASE" "SYNTH" "TOMATCH" n "EQN" False O "EQN" True S _ natProp nat eq nat O S n eq_ind nat S n nat IsSucc n0 I O sym_eq nat O S n H nat not eq nat O S n Add Auto Marker nat nat_ind nat not eq nat n0 S n0 O_S O nat not eq nat n0 S n0 not_eq_S n0 S n0 H n nat not eq nat n S n Add Auto Marker plus plus nat n natnat nat "MULTCASE" "SYNTH" "TOMATCH" n "EQN" m O "EQN" S plus p m S p nat natnat nat nat_ind nat eq nat n0 plus n0 O refl_equal nat O nat eq nat n0 plus n0 O eq_S n0 plus n0 O H n nat eq nat n plus n O Add Auto Marker nat nat_ind nat eq nat S plus n0 n plus n0 S n refl_equal nat S n nat eq nat S plus n0 n plus n0 S n eq_S S plus n0 n plus n0 S n H m nat nat eq nat S plus n m plus n S m Add Auto Marker mult mult nat n natnat nat "MULTCASE" "SYNTH" "TOMATCH" n "EQN" O O "EQN" plus m mult p m S p nat natnat nat nat_ind nat eq nat O mult n0 O refl_equal nat O nat eq nat O mult n0 O H n nat eq nat O mult n O Add Auto Marker nat nat_ind nat eq nat plus mult n0 m n0 mult n0 S m refl_equal nat O nat eq nat plus mult p m p mult p S m "MULTCASE" nat eq nat plus plus m mult p m S p S plus m n0 "TOMATCH" H "EQN" eq_ind nat S plus plus m mult p m p nat eq nat n0 S plus m plus mult p m p eq_S plus plus m mult p m p plus m plus mult p m p nat_ind nat eq nat plus plus n0 mult p m p plus n0 plus mult p m p refl_equal nat plus mult p m p nat eq nat plus plus n0 mult p m p plus n0 plus mult p m p eq_S plus plus n0 . p plus n0 plus . p H0 m plus plus m mult p m S p plus_n_Sm plus m mult p m p refl_equal n nat nat eq nat plus mult n m n mult n S m Add Auto Marker Inductive le [n:nat] : natProp := le_n : le n n | le_S : nat le n m le n S m nat natProp P n nat le n m P m P S m F F nat n0 le n n0 l P n0 "MULTCASE" P "TOMATCH" l "EQN" f le_n "EQN" f0 m l0 F m l0 le_S m l0 nat natProp P n nat le n m P m P S m nat le n n0 P n0 Add Auto Marker nat le S n m nat natProp Add Auto Marker nat le m n nat natProp Add Auto Marker nat lt m n nat natProp Add Auto Marker nat nat_ind nat natProp P O nat P S m P n0 natProp P O nat P S m H nat natProp P O nat P S m P n0 natProp P O nat P S m H1 n0 n nat natProp P O nat P S m P n nat natProp nat R O n nat R S n O nat nat R n m R S n S m nat nat_ind nat nat R n0 m H nat nat R n0 m nat nat_ind nat . H0 n0 nat . m n nat natProp nat R O n nat R S n O nat nat R n m R S n S m nat nat R n m
>>>>>>> Export LogicSyntax >>>>>>> Export Specif Grammar Marker Grammar Marker Syntax Marker
>>>>>>> Export Logic >>>>>>> Import LogicSyntax
Inductive sig [A:Set; P:AProp] : Set := exist : A P x sig A P Set AProp #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P Prop A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 exist x x0 Set AProp #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P Prop A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P P0 s Set AProp #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P Set A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 exist x x0 Set AProp #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P Set A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P P0 s Set AProp #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P #Subsets#Specif#sig_rect.obj 7 A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 exist x x0 Set AProp #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P #Subsets#Specif#sig_rect.obj 7 A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sig.cci 0) A P P0 s Inductive sig2 [A:Set; P:AProp; Q:AProp] : Set := exist2 : A P x Q x sig2 A P Q Set AProp #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q Prop A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 exist2 x x0 x1 Set AProp AProp #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q Prop A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q P0 s Set AProp #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q Set A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 exist2 x x0 x1 Set AProp AProp #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q Set A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q P0 s Set AProp #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q #Subsets#Specif#sig2_rect.obj 28 A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 exist2 x x0 x1 Set AProp AProp #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q #Subsets#Specif#sig2_rect.obj 28 A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sig2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sig2.cci 0) A P Q P0 s Inductive sigS [A:Set; P:ASet] : Set := existS : A P x sigS A P Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P Prop A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 existS x x0 Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P Prop A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P P0 s Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P Set A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 existS x x0 Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P Set A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P P0 s Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P #Subsets#Specif#sigS_rect.obj 52 A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 existS x x0 Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P #Subsets#Specif#sigS_rect.obj 52 A P x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS.cci 0 1) A P x y #GENTERM (MUTIND #Subsets#Specif#sigS.cci 0) A P P0 s Inductive sigS2 [A:Set; P:ASet; Q:ASet] : Set := existS2 : A P x Q x sigS2 A P Q Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q Prop A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 existS2 x x0 x1 Set ASet ASet #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q Prop A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q P0 s Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q Set A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 existS2 x x0 x1 Set ASet ASet #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q Set A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q P0 s Set ASet #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q #Subsets#Specif#sigS2_rect.obj 73 A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 existS2 x x0 x1 Set ASet ASet #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q #Subsets#Specif#sigS2_rect.obj 73 A P x Q x P0 #GENTERM (MUTCONSTRUCT #Subsets#Specif#sigS2.cci 0 1) A P Q x y y0 #GENTERM (MUTIND #Subsets#Specif#sigS2.cci 0) A P Q P0 s
Inductive sig [A:Set; P:AProp] : Set := exist : A P x sig A P Set AProp sig A P Prop A P x P0 exist A P x y sig A P "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 exist x x0 Set AProp sig A P Prop A P x P0 exist A P x y sig A P P0 s Set AProp sig A P Set A P x P0 exist A P x y sig A P "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 exist x x0 Set AProp sig A P Set A P x P0 exist A P x y sig A P P0 s Set AProp sig A P #Subsets#Specif#sig_rect.obj 7 A P x P0 exist A P x y sig A P "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 exist x x0 Set AProp sig A P #Subsets#Specif#sig_rect.obj 7 A P x P0 exist A P x y sig A P P0 s Inductive sig2 [A:Set; P:AProp; Q:AProp] : Set := exist2 : A P x Q x sig2 A P Q Set AProp sig2 A P Q Prop A P x Q x P0 exist2 A P Q x y y0 sig2 A P Q "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 exist2 x x0 x1 Set AProp AProp sig2 A P Q Prop A P x Q x P0 exist2 A P Q x y y0 sig2 A P Q P0 s Set AProp sig2 A P Q Set A P x Q x P0 exist2 A P Q x y y0 sig2 A P Q "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 exist2 x x0 x1 Set AProp AProp sig2 A P Q Set A P x Q x P0 exist2 A P Q x y y0 sig2 A P Q P0 s Set AProp sig2 A P Q #Subsets#Specif#sig2_rect.obj 28 A P x Q x P0 exist2 A P Q x y y0 sig2 A P Q "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 exist2 x x0 x1 Set AProp AProp sig2 A P Q #Subsets#Specif#sig2_rect.obj 28 A P x Q x P0 exist2 A P Q x y y0 sig2 A P Q P0 s Inductive sigS [A:Set; P:ASet] : Set := existS : A P x sigS A P Set ASet sigS A P Prop A P x P0 existS A P x y sigS A P "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 existS x x0 Set ASet sigS A P Prop A P x P0 existS A P x y sigS A P P0 s Set ASet sigS A P Set A P x P0 existS A P x y sigS A P "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 existS x x0 Set ASet sigS A P Set A P x P0 existS A P x y sigS A P P0 s Set ASet sigS A P #Subsets#Specif#sigS_rect.obj 52 A P x P0 existS A P x y sigS A P "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 existS x x0 Set ASet sigS A P #Subsets#Specif#sigS_rect.obj 52 A P x P0 existS A P x y sigS A P P0 s Inductive sigS2 [A:Set; P:ASet; Q:ASet] : Set := existS2 : A P x Q x sigS2 A P Q Set ASet sigS2 A P Q Prop A P x Q x P0 existS2 A P Q x y y0 sigS2 A P Q "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 existS2 x x0 x1 Set ASet ASet sigS2 A P Q Prop A P x Q x P0 existS2 A P Q x y y0 sigS2 A P Q P0 s Set ASet sigS2 A P Q Set A P x Q x P0 existS2 A P Q x y y0 sigS2 A P Q "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 existS2 x x0 x1 Set ASet ASet sigS2 A P Q Set A P x Q x P0 existS2 A P Q x y y0 sigS2 A P Q P0 s Set ASet sigS2 A P Q #Subsets#Specif#sigS2_rect.obj 73 A P x Q x P0 existS2 A P Q x y y0 sigS2 A P Q "FORCELET" "SYNTH" "TOMATCH" s "EQN" f x x0 x1 existS2 x x0 x1 Set ASet ASet sigS2 A P Q #Subsets#Specif#sigS2_rect.obj 73 A P x Q x P0 existS2 A P Q x y y0 sigS2 A P Q P0 s #Specif#_2.obj : Unrecognized object Printing Let #Specif#_3.obj : Unrecognized object Printing Let #Specif#_4.obj : Unrecognized object Printing Let #Specif#_5.obj : Unrecognized object Printing Let
Set AProp sig A P "FORCELET" "SYNTH" "TOMATCH" e "EQN" a exist a _ sig A PA sig A P "FORCELET" sig A P P #GENTERM (CONST #Subset_projections#Specif#proj1_sig.cci P A) e0 "TOMATCH" e "EQN" b exist a b sig A P P #GENTERM (CONST #Subset_projections#Specif#proj1_sig.cci P A) e
Set AProp sig A P "FORCELET" "SYNTH" "TOMATCH" e "EQN" a exist a _ Set AProp sig A P A Set AProp sig A P "FORCELET" sig A P P proj1_sig A P e0 "TOMATCH" e "EQN" b exist a b Set AProp sig A P P proj1_sig A P e
Set ASet sigS A P "FORCELET" "SYNTH" "TOMATCH" x "EQN" a existS a _ sigS A P A sigS A P "FORCELET" sigS A P P #GENTERM (CONST #Projections#Specif#projS1.cci P A) x0 "TOMATCH" x "EQN" h existS x0 h sigS A P P #GENTERM (CONST #Projections#Specif#projS1.cci P A) x
Set ASet sigS A P "FORCELET" "SYNTH" "TOMATCH" x "EQN" a existS a _ Set ASet sigS A P A Set ASet sigS A P "FORCELET" sigS A P P projS1 A P x0 "TOMATCH" x "EQN" h existS x0 h Set ASet sigS A P P projS1 A P x Syntax Macro ProjS1 = projS1 "ISEVAR" "ISEVAR" Syntax Macro ProjS2 = projS2 "ISEVAR" "ISEVAR"
Inductive sumbool [A:Prop; B:Prop] : Set := left : A sumbool A B | right : B sumbool A B Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B Prop A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x left x "EQN" f0 x right x Prop Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B Prop A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B P s Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B Set A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x left x "EQN" f0 x right x Prop Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B Set A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B P s Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B #Extended_booleans#Specif#sumbool_rect.obj 7 A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x left x "EQN" f0 x right x Prop Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B #Extended_booleans#Specif#sumbool_rect.obj 7 A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumbool.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumbool.cci 0) A B P s Inductive sumor [A:Set; B:Prop] : Set := inleft : A sumor A B | inright : B sumor A B Set Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B Prop A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inleft x "EQN" f0 x inright x Set Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B Prop A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B P s Set Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B Set A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inleft x "EQN" f0 x inright x Set Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B Set A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B P s Set Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B #Extended_booleans#Specif#sumor_rect.obj 29 A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inleft x "EQN" f0 x inright x Set Prop #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B #Extended_booleans#Specif#sumor_rect.obj 29 A P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 1) A B y B P #GENTERM (MUTCONSTRUCT #Extended_booleans#Specif#sumor.cci 0 2) A B y #GENTERM (MUTIND #Extended_booleans#Specif#sumor.cci 0) A B P s
Inductive sumbool [A:Prop; B:Prop] : Set := left : A sumbool A B | right : B sumbool A B Prop sumbool A B Prop A P left A B y B P right A B y sumbool A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x left x "EQN" f0 x right x Prop Prop sumbool A B Prop A P left A B y B P right A B y sumbool A B P s Prop sumbool A B Set A P left A B y B P right A B y sumbool A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x left x "EQN" f0 x right x Prop Prop sumbool A B Set A P left A B y B P right A B y sumbool A B P s Prop sumbool A B #Extended_booleans#Specif#sumbool_rect.obj 7 A P left A B y B P right A B y sumbool A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x left x "EQN" f0 x right x Prop Prop sumbool A B #Extended_booleans#Specif#sumbool_rect.obj 7 A P left A B y B P right A B y sumbool A B P s Inductive sumor [A:Set; B:Prop] : Set := inleft : A sumor A B | inright : B sumor A B Set Prop sumor A B Prop A P inleft A B y B P inright A B y sumor A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inleft x "EQN" f0 x inright x Set Prop sumor A B Prop A P inleft A B y B P inright A B y sumor A B P s Set Prop sumor A B Set A P inleft A B y B P inright A B y sumor A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inleft x "EQN" f0 x inright x Set Prop sumor A B Set A P inleft A B y B P inright A B y sumor A B P s Set Prop sumor A B #Extended_booleans#Specif#sumor_rect.obj 29 A P inleft A B y B P inright A B y sumor A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inleft x "EQN" f0 x inright x Set Prop sumor A B #Extended_booleans#Specif#sumor_rect.obj 29 A P inleft A B y B P inright A B y sumor A B P s
Set Set S S'Prop S S'Set SProp SProp S sig S' S' R x y exist SS' SS' S R z f z S "FORCELET" "SYNTH" "TOMATCH" H z "EQN" y exist y _ S sig_ind S' S' R z y sig S' S' R z y R z "FORCELET" "SYNTH" "TOMATCH" s "EQN" y exist y _ S' R z x y H z S sig S' S' R x y sig SS' SS' S R z f z S sigS S' S' R' x y existS SS' SS' S R' z f z S "FORCELET" "SYNTH" "TOMATCH" H z "EQN" y existS y _ S sigS_rec S' S' R' z y sigS S' S' R' z y R' z "FORCELET" "SYNTH" "TOMATCH" s "EQN" y existS y _ S' R' z x y H z S sigS S' S' R' x y sigS SS' SS' S R' z f z S sumbool R1 x R2 x exist Sbool Sbool S or and eq bool f x true R1 x and eq bool f x false R2 x S "MULTCASE" "SYNTH" "TOMATCH" H z "EQN" true left _ "EQN" false right _ S sumbool_ind R1 z R2 z sumbool R1 z R2 z or and eq bool "MULTCASE" "SYNTH" "TOMATCH" s "EQN" true left _ "EQN" false right _ true R1 z and eq bool "MULTCASE" "SYNTH" "TOMATCH" s "EQN" true left _ "EQN" false right _ false R2 z R1 z or_introl and eq bool true true R1 z and eq bool true false R2 z conj eq bool true true R1 z refl_equal bool true y R2 z or_intror and eq bool false true R1 z and eq bool false false R2 z conj eq bool false false R2 z refl_equal bool false y H z S sumbool R1 x R2 x sig Sbool Sbool S or and eq bool f x true R1 x and eq bool f x false R2 x
Set Set S S'Prop S sig S' S' R x y sig SS' SS' S R z f z Set Set S S'Set S sigS S' S' R' x y sigS SS' SS' S R' z f z Set SProp SProp S sumbool R1 x R2 x sig Sbool Sbool S or and eq bool f x true R1 x and eq bool f x false R2 x
Inductive Exc [A:Set] : Set := value : A Exc A | error : Exc A Set #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A Prop A P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 1) A y P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 2) A #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x value x "EQN" f0 error Set #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A Prop A P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 1) A y P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 2) A #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A P e Set #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A Set A P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 1) A y P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 2) A #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x value x "EQN" f0 error Set #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A Set A P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 1) A y P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 2) A #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A P e Set #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A #Exceptions#Specif#Exc_rect.obj 7 A P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 1) A y P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 2) A #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x value x "EQN" f0 error Set #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A #Exceptions#Specif#Exc_rect.obj 7 A P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 1) A y P #GENTERM (MUTCONSTRUCT #Exceptions#Specif#Exc.cci 0 2) A #GENTERM (MUTIND #Exceptions#Specif#Exc.cci 0) A P e
Inductive Exc [A:Set] : Set := value : A Exc A | error : Exc A Set Exc A Prop A P value A y P error A Exc A "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x value x "EQN" f0 error Set Exc A Prop A P value A y P error A Exc A P e Set Exc A Set A P value A y P error A Exc A "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x value x "EQN" f0 error Set Exc A Set A P value A y P error A Exc A P e Set Exc A #Exceptions#Specif#Exc_rect.obj 7 A P value A y P error A Exc A "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x value x "EQN" f0 error Set Exc A #Exceptions#Specif#Exc_rect.obj 7 A P value A y P error A Exc A P e Syntax Macro Error = error "ISEVAR" Syntax Macro Value = value "ISEVAR" *** [ False_rec : Set FalseP ] #Specif#False_rect.obj 4 False "MULTCASE" Empty_set C "TOMATCH" False_rec Empty_set H #Specif#False_rect.obj 7 FalseC False_rec Set FalseP Syntax Macro Except = except "ISEVAR" Prop Set A not A False_rec C h2 h1 Prop Set A not A C Prop Set A BC and A B F and_ind A B A A B H AB and_ind A B B A B H0 AB Prop Prop Set A BC and A B C Add Auto Marker Inductive sigT [A:#Specif#sigT.obj 19; P: A #Specif#sigT.obj 18 ] : #Specif#sigT.obj 17 := existT : A P x sigT A P #Specif#sigT.obj 19 A #Specif#sigT.obj 18 sigT A P Prop A P x P0 existT A P x y sigT A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 existT x x0 #Specif#sigT.obj 19 A #Specif#sigT.obj 18 sigT A P Prop A P x P0 existT A P x y sigT A P P0 s #Specif#sigT.obj 19 A #Specif#sigT.obj 18 sigT A P Set A P x P0 existT A P x y sigT A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 existT x x0 #Specif#sigT.obj 19 A #Specif#sigT.obj 18 sigT A P Set A P x P0 existT A P x y sigT A P P0 s #Specif#sigT.obj 19 A #Specif#sigT.obj 18 sigT A P #Specif#sigT_rect.obj 102 A P x P0 existT A P x y sigT A P "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x x0 existT x x0 #Specif#sigT.obj 19 A #Specif#sigT.obj 18 sigT A P #Specif#sigT_rect.obj 102 A P x P0 existT A P x y sigT A P P0 s
#projections_sigT#Specif#A.obj 156 A #projections_sigT#Specif#P.obj 161 sigT A P "MULTCASE" "SYNTH" "TOMATCH" H "EQN" x existT x _ sigT A P A sigT A P "MULTCASE" sigT A P P #GENTERM (CONST #projections_sigT#Specif#projT1.cci P A) H0 "TOMATCH" H "EQN" h existT x h sigT A P P #GENTERM (CONST #projections_sigT#Specif#projT1.cci P A) H
Universes of #Specif#projections_sigT#A.obj (6 uni,4 edges) Universes of #Specif#projections_sigT#P.obj (9 uni,7 edges) #projections_sigT#Specif#A.obj 156 A #projections_sigT#Specif#P.obj 161 sigT A P "MULTCASE" "SYNTH" "TOMATCH" H "EQN" x existT x _ #projections_sigT#Specif#A.obj 156 A #projections_sigT#Specif#P.obj 161 sigT A P A #projections_sigT#Specif#A.obj 156 A #projections_sigT#Specif#P.obj 161 sigT A P "MULTCASE" sigT A P P projT1 A P H0 "TOMATCH" H "EQN" h existT x h #projections_sigT#Specif#A.obj 156 A #projections_sigT#Specif#P.obj 161 sigT A P P projT1 A P H
>>>>>>> Export Logic Grammar Marker Syntax Marker
>>>>>>> Export Datatypes Inductive True : Prop := I : True Prop P True "MULTCASE" "SYNTH" "TOMATCH" t "EQN" f I Prop P TrueP Set P True "MULTCASE" "SYNTH" "TOMATCH" t "EQN" f I Set P TrueP Inductive False : Prop := Prop False "MULTCASE" P "TOMATCH" f Prop FalseP Prop AFalse PropProp
Inductive and [A:Prop; B:Prop] : Prop := conj : A B and A B Prop A BP #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" a "EQN" f x x0 conj x x0 Prop Prop Prop A BP #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B P Prop Set A BP #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" a "EQN" f x x0 conj x x0 Prop Prop Set A BP #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B P Prop Prop #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B #GENTERM (CONST #Conjunction#Logic#and_ind.cci) A B A A B H0 H #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B A #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B #GENTERM (CONST #Conjunction#Logic#and_ind.cci) A B B A B H1 H #GENTERM (MUTIND #Conjunction#Logic#and.cci 0) A B B
Inductive and [A:Prop; B:Prop] : Prop := conj : A B and A B Prop A BP and A B "MULTCASE" "SYNTH" "TOMATCH" a "EQN" f x x0 conj x x0 Prop Prop Prop A BP and A B P Prop Set A BP and A B "MULTCASE" "SYNTH" "TOMATCH" a "EQN" f x x0 conj x x0 Prop Prop Set A BP and A B P Prop Prop and A B A Prop Prop and A B B
Inductive or [A:Prop; B:Prop] : Prop := or_introl : A or A B | or_intror : B or A B Prop AP BP #GENTERM (MUTIND #Disjunction#Logic#or.cci 0) A B "MULTCASE" "SYNTH" "TOMATCH" o "EQN" f x or_introl x "EQN" f0 x or_intror x Prop Prop Prop AP BP #GENTERM (MUTIND #Disjunction#Logic#or.cci 0) A B P
Inductive or [A:Prop; B:Prop] : Prop := or_introl : A or A B | or_intror : B or A B Prop AP BP or A B "MULTCASE" "SYNTH" "TOMATCH" o "EQN" f x or_introl x "EQN" f0 x or_intror x Prop Prop Prop AP BP or A B P
Prop and PQ QP Prop PropProp
Prop and PQ QP Prop PropProp Prop or and P Q and not P R Prop Prop PropProp
Inductive ex [A:Set; P:AProp] : Prop := ex_intro : A P x ex A P Set AProp Prop A P x P0 #GENTERM (MUTIND #First_order_quantifiers#Logic#ex.cci 0) A P "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x x0 ex_intro x x0 Set AProp Prop A P x P0 #GENTERM (MUTIND #First_order_quantifiers#Logic#ex.cci 0) A P P0 Inductive ex2 [A:Set; P:AProp; Q:AProp] : Prop := ex_intro2 : A P x Q x ex2 A P Q Set AProp Prop A P x Q x P0 #GENTERM (MUTIND #First_order_quantifiers#Logic#ex2.cci 0) A P Q "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x x0 x1 ex_intro2 x x0 x1 Set AProp AProp Prop A P x Q x P0 #GENTERM (MUTIND #First_order_quantifiers#Logic#ex2.cci 0) A P Q P0 Set AProp A P x Set AProp Prop
Inductive ex [A:Set; P:AProp] : Prop := ex_intro : A P x ex A P Set AProp Prop A P x P0 ex A P "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x x0 ex_intro x x0 Set AProp Prop A P x P0 ex A P P0 Inductive ex2 [A:Set; P:AProp; Q:AProp] : Prop := ex_intro2 : A P x Q x ex2 A P Q Set AProp Prop A P x Q x P0 ex2 A P Q "MULTCASE" "SYNTH" "TOMATCH" e "EQN" f x x0 x1 ex_intro2 x x0 x1 Set AProp AProp Prop A P x Q x P0 ex2 A P Q P0 Set AProp A P x Set AProp Prop
Inductive eq [A:Set; x:A] : AProp := refl_equal : eq A x x Set A AProp P x A #GENTERM (MUTIND #Equality#Logic#eq.cci 0) A x y "MULTCASE" P "TOMATCH" e "EQN" f refl_equal Set A AProp P x A #GENTERM (MUTIND #Equality#Logic#eq.cci 0) A x y P y Set A ASet P x A #GENTERM (MUTIND #Equality#Logic#eq.cci 0) A x y "MULTCASE" P "TOMATCH" e "EQN" f refl_equal Set A ASet P x A #GENTERM (MUTIND #Equality#Logic#eq.cci 0) A x y P y
Inductive eq [A:Set; x:A] : AProp := refl_equal : eq A x x Set A AProp P x A eq A x y "MULTCASE" P "TOMATCH" e "EQN" f refl_equal Set A AProp P x A eq A x y P y Set A ASet P x A eq A x y "MULTCASE" P "TOMATCH" e "EQN" f refl_equal Set A ASet P x A eq A x y P y Add Auto Marker
Prop A AFalse False_ind C h2 h1 Prop Prop A not A C
Set Set AB A A A eq A x y eq_ind A x A eq A a x refl_equal A x y H eq A x y eq A y x eq A x y eq A y z eq_ind A y A eq A x a H z H0 eq A x y eq A y z eq A x z eq A x y eq_ind A x A eq B f x f a refl_equal B f x y H eq A x y eq B f x f y Set A BC A B eq A x1 y1 eq_ind A x1 A eq B x2 y2 eq C . . eq B x2 y2 eq_ind B x2 B . refl_equal C f0 x1 x2 y2 H0 y1 H Set A BC A A B B eq A x1 y1 eq B x2 y2 eq C f x1 x2 f y1 y2 not eq A x y eq A y x h1 eq_ind A y A eq A a y refl_equal A y x h2 not eq A x y not eq A y x #GENTERM (CONST #equality#Logic_lemmas#Logic#sym_eq.cci y x A) eq A x y eq A y x #GENTERM (CONST #equality#Logic_lemmas#Logic#sym_not_eq.cci y x A) not eq A x y not eq A y x #GENTERM (CONST #equality#Logic_lemmas#Logic#trans_eq.cci z y x A) eq A x y eq A y z eq A x z
Set A A eq A x y eq A y x Set A A A eq A x y eq A y z eq A x z Set Set AB A A eq A x y eq B f x f y Set Set Set A BC A A B B eq A x1 y1 .. Set A A not eq A x y not eq A y x Set A A #GENTERM (CONST #Logic_lemmas#Logic#sym_eq.cci) A x y Set A A eq A x y eq A y x Set A A #GENTERM (CONST #Logic_lemmas#Logic#sym_not_eq.cci) A x y Set A A not eq A x y not eq A y x Set A A A #GENTERM (CONST #Logic_lemmas#Logic#trans_eq.cci) A x y z Set A A A eq A x y eq A y z eq A x z Set A A #Logic_lemmas#Logic#eq_rect.obj 5 P x A eq A x y "MULTCASE" A identity A x y0 P y0 "TOMATCH" eq_rec A x A identity A x a refl_identity A x y H "EQN" X refl_identity Set A A #Logic_lemmas#Logic#eq_rect.obj 10 P x A eq A x y P y Set A AProp P x A eq A y x "MULTCASE" A P a "TOMATCH" #GENTERM (CONST #Logic_lemmas#Logic#sym_eq.cci) A y x H0 "EQN" H refl_equal Set A AProp P x A eq A y x P y Set A ASet P x A eq A y x "MULTCASE" A P a "TOMATCH" #GENTERM (CONST #Logic_lemmas#Logic#sym_eq.cci) A y x H0 "EQN" H refl_equal Set A ASet P x A eq A y x P y Set A A #Logic_lemmas#Logic#eq_rect_r.obj 31 P x A eq A y x #GENTERM (CONST #Logic_lemmas#Logic#eq_rect.cci) A x A P a H y #GENTERM (CONST #Logic_lemmas#Logic#sym_eq.cci) A y x H0 Set A A #Logic_lemmas#Logic#eq_rect_r.obj 38 P x A eq A y x P y
Prop Prop A not A C Set A A eq A x y eq A y x Set A A A eq A x y eq A y z eq A x z Set Set AB A A eq A x y eq B f x f y Set Set Set A BC A A B B eq A x1 y1 . . Set A A not eq A x y not eq A y x Set A sym_eq A x y Set A A eq A x y eq A y x Set A sym_not_eq A x y Set A A not eq A x y not eq A y x Set A trans_eq A x y z Set A A A eq A x y eq A y z eq A x z Set A A #Logic_lemmas#Logic#eq_rect.obj 10 P x A eq A x y P y Set A AProp P x A eq A y x "MULTCASE" A P a "TOMATCH" sym_eq A y x H0 "EQN" H refl_equal Set A AProp P x A eq A y x P y Set A ASet P x A eq A y x "MULTCASE" A P a "TOMATCH" sym_eq A y x H0 "EQN" H refl_equal Set A ASet P x A eq A y x P y Set A A #Logic_lemmas#Logic#eq_rect_r.obj 31 P x A eq A y x eq_rect A x A P a H y sym_eq A y x H0 Set A A #Logic_lemmas#Logic#eq_rect_r.obj 38 P x A eq A y x P y Add Auto Marker Syntax Macro Ex = ex "ISEVAR" Syntax Macro Ex2 = ex2 "ISEVAR" Syntax Macro All = all "ISEVAR"
>>>>>>> Export Datatypes Grammar Marker Syntax Marker
Inductive unit : Set := tt : unit unitProp P tt unit "MULTCASE" "SYNTH" "TOMATCH" u "EQN" f tt unitProp P tt unit P u unitSet P tt unit "MULTCASE" "SYNTH" "TOMATCH" u "EQN" f tt unitSet P tt unit P u unit #Datatypes#unit_rect.obj 4 P tt unit "MULTCASE" "SYNTH" "TOMATCH" u "EQN" f tt unit #Datatypes#unit_rect.obj 4 P tt unit P u Inductive bool : Set := true : bool | false : bool boolProp P true P false bool "SYNTH" b f f0 boolProp P true P false bool P b boolSet P true P false bool "SYNTH" b f f0 boolSet P true P false bool P b bool #Datatypes#bool_rect.obj 14 P true P false bool "SYNTH" b f f0 bool #Datatypes#bool_rect.obj 14 P true P false bool P b #Datatypes#_0.obj : Unrecognized object Printing If Inductive nat : Set := O : nat | S : natnat natProp P O nat P n P S n F F nat n P n "MULTCASE" "SYNTH" "TOMATCH" n "EQN" f O "EQN" f0 n0 F n0 S n0 natProp P O nat P n P S n nat P n natSet P O nat P n P S n F F nat n P n "MULTCASE" "SYNTH" "TOMATCH" n "EQN" f O "EQN" f0 n0 F n0 S n0 natSet P O nat P n P S n nat P n nat #Datatypes#nat_rect.obj 25 P O nat P n P S n F F nat n P n "MULTCASE" "SYNTH" "TOMATCH" n "EQN" f O "EQN" f0 n0 F n0 S n0 nat #Datatypes#nat_rect.obj 25 P O nat P n P S n nat P n Inductive Empty_set : Set := Empty_setProp Empty_set "MULTCASE" P "TOMATCH" e Empty_setProp Empty_set P e Empty_setSet Empty_set "MULTCASE" P "TOMATCH" e Empty_setSet Empty_set P e Empty_set #Datatypes#Empty_set_rect.obj 41 Empty_set "MULTCASE" P "TOMATCH" e Empty_set #Datatypes#Empty_set_rect.obj 41 Empty_set P e Inductive identity [A:Set; a:A] : ASet := refl_identity : identity A a a Set A A identity A a y Prop P a refl_identity A a A identity A a y "MULTCASE" P "TOMATCH" i "EQN" f refl_identity Set A A identity A a y Prop P a refl_identity A a A identity A a y P y i Set A A identity A a y Set P a refl_identity A a A identity A a y "MULTCASE" P "TOMATCH" i "EQN" f refl_identity Set A A identity A a y Set P a refl_identity A a A identity A a y P y i Set A A identity A a y #Datatypes#identity_rect.obj 53 P a refl_identity A a A identity A a y "MULTCASE" P "TOMATCH" i "EQN" f refl_identity Set A A identity A a y #Datatypes#identity_rect.obj 53 P a refl_identity A a A identity A a y P y i Add Auto Marker Inductive sum [A:Set; B:Set] : Set := inl : A sum A B | inr : B sum A B Set sum A B Prop A P inl A B y B P inr A B y sum A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inl x "EQN" f0 x inr x Set Set sum A B Prop A P inl A B y B P inr A B y sum A B P s Set sum A B Set A P inl A B y B P inr A B y sum A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inl x "EQN" f0 x inr x Set Set sum A B Set A P inl A B y B P inr A B y sum A B P s Set sum A B #Datatypes#sum_rect.obj 73 A P inl A B y B P inr A B y sum A B "MULTCASE" "SYNTH" "TOMATCH" s "EQN" f x inl x "EQN" f0 x inr x Set Set sum A B #Datatypes#sum_rect.obj 73 A P inl A B y B P inr A B y sum A B P s Inductive prod [A:Set; B:Set] : Set := pair : A B prod A B Set prod A B Prop A B P pair A B y y0 prod A B "FORCELET" "SYNTH" "TOMATCH" p "EQN" f x x0 pair x x0 Set Set prod A B Prop A B P pair A B y y0 prod A B P p Set prod A B Set A B P pair A B y y0 prod A B "FORCELET" "SYNTH" "TOMATCH" p "EQN" f x x0 pair x x0 Set Set prod A B Set A B P pair A B y y0 prod A B P p Set prod A B #Datatypes#prod_rect.obj 95 A B P pair A B y y0 prod A B "FORCELET" "SYNTH" "TOMATCH" p "EQN" f x x0 pair x x0 Set Set prod A B #Datatypes#prod_rect.obj 95 A B P pair A B y y0 prod A B P p #Datatypes#_2.obj : Unrecognized object Printing Let
Set Set prod A B "FORCELET" "SYNTH" "TOMATCH" p "EQN" x pair x _ prod A B A prod A B "FORCELET" "SYNTH" "TOMATCH" p "EQN" y pair _ y prod A B B
Set Set prod A B "FORCELET" "SYNTH" "TOMATCH" p "EQN" x pair x _ Set Set prod A B A Set Set prod A B "FORCELET" "SYNTH" "TOMATCH" p "EQN" y pair _ y Set Set prod A B B Syntax Macro Fst = fst "ISEVAR" "ISEVAR" Syntax Macro Snd = snd "ISEVAR" "ISEVAR" Add Auto Marker
#Core#let.obj : Unrecognized object ABSTRACTION
Syntax Marker Syntax Marker Syntax Marker