From 9a6e3fe764dc2543dfa94de20fe5eec42d6be705 Mon Sep 17 00:00:00 2001 From: herbelin Date: Sat, 29 Nov 2003 17:28:49 +0000 Subject: Remplacement des fichiers .v ancienne syntaxe de theories, contrib et states par les fichiers nouvelle syntaxe git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@5027 85f007b7-540e-0410-9357-904b9bb8a0f7 --- contrib/correctness/Tuples.v | 148 ++++++++++++++++++++----------------------- 1 file changed, 70 insertions(+), 78 deletions(-) (limited to 'contrib/correctness/Tuples.v') diff --git a/contrib/correctness/Tuples.v b/contrib/correctness/Tuples.v index f9a3b56b7..41ff10c04 100644 --- a/contrib/correctness/Tuples.v +++ b/contrib/correctness/Tuples.v @@ -12,95 +12,87 @@ (* Tuples *) -Definition tuple_1 := [X:Set]X. +Definition tuple_1 (X:Set) := X. Definition tuple_2 := prod. Definition Build_tuple_2 := pair. Definition proj_2_1 := fst. Definition proj_2_2 := snd. -Record tuple_3 [ T1,T2,T3 : Set ] : Set := - { proj_3_1 : T1 ; - proj_3_2 : T2 ; - proj_3_3 : T3 }. - -Record tuple_4 [ T1,T2,T3,T4 : Set ] : Set := - { proj_4_1 : T1 ; - proj_4_2 : T2 ; - proj_4_3 : T3 ; - proj_4_4 : T4 }. - -Record tuple_5 [ T1,T2,T3,T4,T5 : Set ] : Set := - { proj_5_1 : T1 ; - proj_5_2 : T2 ; - proj_5_3 : T3 ; - proj_5_4 : T4 ; - proj_5_5 : T5 }. - -Record tuple_6 [ T1,T2,T3,T4,T5,T6 : Set ] : Set := - { proj_6_1 : T1 ; - proj_6_2 : T2 ; - proj_6_3 : T3 ; - proj_6_4 : T4 ; - proj_6_5 : T5 ; - proj_6_6 : T6 }. - -Record tuple_7 [ T1,T2,T3,T4,T5,T6,T7 : Set ] : Set := - { proj_7_1 : T1 ; - proj_7_2 : T2 ; - proj_7_3 : T3 ; - proj_7_4 : T4 ; - proj_7_5 : T5 ; - proj_7_6 : T6 ; - proj_7_7 : T7 }. +Record tuple_3 (T1 T2 T3:Set) : Set := + {proj_3_1 : T1; proj_3_2 : T2; proj_3_3 : T3}. +Record tuple_4 (T1 T2 T3 T4:Set) : Set := + {proj_4_1 : T1; proj_4_2 : T2; proj_4_3 : T3; proj_4_4 : T4}. -(* Existentials *) - -Definition sig_1 := sig. -Definition exist_1 := exist. - -Inductive sig_2 [ T1,T2 : Set; P:T1->T2->Prop ] : Set := - exist_2 : (x1:T1)(x2:T2)(P x1 x2) -> (sig_2 T1 T2 P). - -Inductive sig_3 [ T1,T2,T3 : Set; P:T1->T2->T3->Prop ] : Set := - exist_3 : (x1:T1)(x2:T2)(x3:T3)(P x1 x2 x3) -> (sig_3 T1 T2 T3 P). +Record tuple_5 (T1 T2 T3 T4 T5:Set) : Set := + {proj_5_1 : T1; proj_5_2 : T2; proj_5_3 : T3; proj_5_4 : T4; proj_5_5 : T5}. +Record tuple_6 (T1 T2 T3 T4 T5 T6:Set) : Set := + {proj_6_1 : T1; + proj_6_2 : T2; + proj_6_3 : T3; + proj_6_4 : T4; + proj_6_5 : T5; + proj_6_6 : T6}. -Inductive sig_4 [ T1,T2,T3,T4 : Set; - P:T1->T2->T3->T4->Prop ] : Set := - exist_4 : (x1:T1)(x2:T2)(x3:T3)(x4:T4) - (P x1 x2 x3 x4) - -> (sig_4 T1 T2 T3 T4 P). +Record tuple_7 (T1 T2 T3 T4 T5 T6 T7:Set) : Set := + {proj_7_1 : T1; + proj_7_2 : T2; + proj_7_3 : T3; + proj_7_4 : T4; + proj_7_5 : T5; + proj_7_6 : T6; + proj_7_7 : T7}. -Inductive sig_5 [ T1,T2,T3,T4,T5 : Set; - P:T1->T2->T3->T4->T5->Prop ] : Set := - exist_5 : (x1:T1)(x2:T2)(x3:T3)(x4:T4)(x5:T5) - (P x1 x2 x3 x4 x5) - -> (sig_5 T1 T2 T3 T4 T5 P). -Inductive sig_6 [ T1,T2,T3,T4,T5,T6 : Set; - P:T1->T2->T3->T4->T5->T6->Prop ] : Set := - exist_6 : (x1:T1)(x2:T2)(x3:T3)(x4:T4)(x5:T5)(x6:T6) - (P x1 x2 x3 x4 x5 x6) - -> (sig_6 T1 T2 T3 T4 T5 T6 P). - -Inductive sig_7 [ T1,T2,T3,T4,T5,T6,T7 : Set; - P:T1->T2->T3->T4->T5->T6->T7->Prop ] : Set := - exist_7 : (x1:T1)(x2:T2)(x3:T3)(x4:T4)(x5:T5)(x6:T6)(x7:T7) - (P x1 x2 x3 x4 x5 x6 x7) - -> (sig_7 T1 T2 T3 T4 T5 T6 T7 P). - -Inductive sig_8 [ T1,T2,T3,T4,T5,T6,T7,T8 : Set; - P:T1->T2->T3->T4->T5->T6->T7->T8->Prop ] : Set := - exist_8 : (x1:T1)(x2:T2)(x3:T3)(x4:T4)(x5:T5)(x6:T6)(x7:T7)(x8:T8) - (P x1 x2 x3 x4 x5 x6 x7 x8) - -> (sig_8 T1 T2 T3 T4 T5 T6 T7 T8 P). - -Inductive dep_tuple_2 [ T1,T2 : Set; P:T1->T2->Set ] : Set := - Build_dep_tuple_2 : (x1:T1)(x2:T2)(P x1 x2) -> (dep_tuple_2 T1 T2 P). +(* Existentials *) -Inductive dep_tuple_3 [ T1,T2,T3 : Set; P:T1->T2->T3->Set ] : Set := - Build_dep_tuple_3 : (x1:T1)(x2:T2)(x3:T3)(P x1 x2 x3) - -> (dep_tuple_3 T1 T2 T3 P). +Definition sig_1 := sig. +Definition exist_1 := exist. +Inductive sig_2 (T1 T2:Set) (P:T1 -> T2 -> Prop) : Set := + exist_2 : forall (x1:T1) (x2:T2), P x1 x2 -> sig_2 T1 T2 P. + +Inductive sig_3 (T1 T2 T3:Set) (P:T1 -> T2 -> T3 -> Prop) : Set := + exist_3 : forall (x1:T1) (x2:T2) (x3:T3), P x1 x2 x3 -> sig_3 T1 T2 T3 P. + + +Inductive sig_4 (T1 T2 T3 T4:Set) (P:T1 -> T2 -> T3 -> T4 -> Prop) : Set := + exist_4 : + forall (x1:T1) (x2:T2) (x3:T3) (x4:T4), + P x1 x2 x3 x4 -> sig_4 T1 T2 T3 T4 P. + +Inductive sig_5 (T1 T2 T3 T4 T5:Set) (P:T1 -> T2 -> T3 -> T4 -> T5 -> Prop) : +Set := + exist_5 : + forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5), + P x1 x2 x3 x4 x5 -> sig_5 T1 T2 T3 T4 T5 P. + +Inductive sig_6 (T1 T2 T3 T4 T5 T6:Set) +(P:T1 -> T2 -> T3 -> T4 -> T5 -> T6 -> Prop) : Set := + exist_6 : + forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5) + (x6:T6), P x1 x2 x3 x4 x5 x6 -> sig_6 T1 T2 T3 T4 T5 T6 P. + +Inductive sig_7 (T1 T2 T3 T4 T5 T6 T7:Set) +(P:T1 -> T2 -> T3 -> T4 -> T5 -> T6 -> T7 -> Prop) : Set := + exist_7 : + forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5) + (x6:T6) (x7:T7), + P x1 x2 x3 x4 x5 x6 x7 -> sig_7 T1 T2 T3 T4 T5 T6 T7 P. + +Inductive sig_8 (T1 T2 T3 T4 T5 T6 T7 T8:Set) +(P:T1 -> T2 -> T3 -> T4 -> T5 -> T6 -> T7 -> T8 -> Prop) : Set := + exist_8 : + forall (x1:T1) (x2:T2) (x3:T3) (x4:T4) (x5:T5) + (x6:T6) (x7:T7) (x8:T8), + P x1 x2 x3 x4 x5 x6 x7 x8 -> sig_8 T1 T2 T3 T4 T5 T6 T7 T8 P. + +Inductive dep_tuple_2 (T1 T2:Set) (P:T1 -> T2 -> Set) : Set := + Build_dep_tuple_2 : + forall (x1:T1) (x2:T2), P x1 x2 -> dep_tuple_2 T1 T2 P. + +Inductive dep_tuple_3 (T1 T2 T3:Set) (P:T1 -> T2 -> T3 -> Set) : Set := + Build_dep_tuple_3 : + forall (x1:T1) (x2:T2) (x3:T3), P x1 x2 x3 -> dep_tuple_3 T1 T2 T3 P. -- cgit v1.2.3