diff options
author | mohring <mohring@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2005-11-30 10:05:53 +0000 |
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committer | mohring <mohring@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2005-11-30 10:05:53 +0000 |
commit | 596f0f2b5ab76305447ed1ef3999fd7d9939fbef (patch) | |
tree | 29becb9e5247f3efa70d08bc2e759c2017e50cfa | |
parent | ffd14d29ba11cffd409f4dced7f23ad5afcb2111 (diff) |
changement parametres inductifs dans les theories
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@7630 85f007b7-540e-0410-9357-904b9bb8a0f7
-rwxr-xr-x | theories/Init/Wf.v | 4 | ||||
-rwxr-xr-x | theories/Lists/Streams.v | 13 | ||||
-rwxr-xr-x | theories/Relations/Relation_Operators.v | 14 | ||||
-rwxr-xr-x | theories/Sets/Relations_2.v | 24 | ||||
-rwxr-xr-x | theories/Sets/Relations_3.v | 4 |
5 files changed, 29 insertions, 30 deletions
diff --git a/theories/Init/Wf.v b/theories/Init/Wf.v index 584e68657..5a05f7b65 100755 --- a/theories/Init/Wf.v +++ b/theories/Init/Wf.v @@ -29,8 +29,8 @@ Section Well_founded. (** The accessibility predicate is defined to be non-informative *) - Inductive Acc : A -> Prop := - Acc_intro : forall x:A, (forall y:A, R y x -> Acc y) -> Acc x. + Inductive Acc (x: A) : Prop := + Acc_intro : (forall y:A, R y x -> Acc y) -> Acc x. Lemma Acc_inv : forall x:A, Acc x -> forall y:A, R y x -> Acc y. destruct 1; trivial. diff --git a/theories/Lists/Streams.v b/theories/Lists/Streams.v index f69041eb8..366172381 100755 --- a/theories/Lists/Streams.v +++ b/theories/Lists/Streams.v @@ -71,9 +71,8 @@ Qed. (** Extensional Equality between two streams *) -CoInductive EqSt : Stream -> Stream -> Prop := +CoInductive EqSt (s1 s2: Stream) : Prop := eqst : - forall s1 s2:Stream, hd s1 = hd s2 -> EqSt (tl s1) (tl s2) -> EqSt s1 s2. (** A coinduction principle *) @@ -140,12 +139,12 @@ Inductive Exists : Stream -> Prop := | Further : forall x:Stream, ~ P x -> Exists (tl x) -> Exists x. i*) -Inductive Exists : Stream -> Prop := - | Here : forall x:Stream, P x -> Exists x - | Further : forall x:Stream, Exists (tl x) -> Exists x. +Inductive Exists ( x: Stream ) : Prop := + | Here : P x -> Exists x + | Further : Exists (tl x) -> Exists x. -CoInductive ForAll : Stream -> Prop := - HereAndFurther : forall x:Stream, P x -> ForAll (tl x) -> ForAll x. +CoInductive ForAll (x: Stream) : Prop := + HereAndFurther : P x -> ForAll (tl x) -> ForAll x. Section Co_Induction_ForAll. diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v index 86cd92b85..b538620d1 100755 --- a/theories/Relations/Relation_Operators.v +++ b/theories/Relations/Relation_Operators.v @@ -25,10 +25,10 @@ Section Transitive_Closure. Variable A : Type. Variable R : relation A. - Inductive clos_trans : A -> A -> Prop := - | t_step : forall x y:A, R x y -> clos_trans x y + Inductive clos_trans (x: A) : A -> Prop := + | t_step : forall y:A, R x y -> clos_trans x y | t_trans : - forall x y z:A, clos_trans x y -> clos_trans y z -> clos_trans x z. + forall y z:A, clos_trans x y -> clos_trans y z -> clos_trans x z. End Transitive_Closure. @@ -36,11 +36,11 @@ Section Reflexive_Transitive_Closure. Variable A : Type. Variable R : relation A. - Inductive clos_refl_trans : relation A := - | rt_step : forall x y:A, R x y -> clos_refl_trans x y - | rt_refl : forall x:A, clos_refl_trans x x + Inductive clos_refl_trans (x:A) : A -> Prop:= + | rt_step : forall y:A, R x y -> clos_refl_trans x y + | rt_refl : clos_refl_trans x x | rt_trans : - forall x y z:A, + forall y z:A, clos_refl_trans x y -> clos_refl_trans y z -> clos_refl_trans x z. End Reflexive_Transitive_Closure. diff --git a/theories/Sets/Relations_2.v b/theories/Sets/Relations_2.v index 918e45ee1..11ac85e84 100755 --- a/theories/Sets/Relations_2.v +++ b/theories/Sets/Relations_2.v @@ -32,18 +32,18 @@ Section Relations_2. Variable U : Type. Variable R : Relation U. -Inductive Rstar : Relation U := - | Rstar_0 : forall x:U, Rstar x x - | Rstar_n : forall x y z:U, R x y -> Rstar y z -> Rstar x z. - -Inductive Rstar1 : Relation U := - | Rstar1_0 : forall x:U, Rstar1 x x - | Rstar1_1 : forall x y:U, R x y -> Rstar1 x y - | Rstar1_n : forall x y z:U, Rstar1 x y -> Rstar1 y z -> Rstar1 x z. - -Inductive Rplus : Relation U := - | Rplus_0 : forall x y:U, R x y -> Rplus x y - | Rplus_n : forall x y z:U, R x y -> Rplus y z -> Rplus x z. +Inductive Rstar (x:U) : U -> Prop := + | Rstar_0 : Rstar x x + | Rstar_n : forall y z:U, R x y -> Rstar y z -> Rstar x z. + +Inductive Rstar1 (x:U) : U -> Prop := + | Rstar1_0 : Rstar1 x x + | Rstar1_1 : forall y:U, R x y -> Rstar1 x y + | Rstar1_n : forall y z:U, Rstar1 x y -> Rstar1 y z -> Rstar1 x z. + +Inductive Rplus (x:U) : U -> Prop := + | Rplus_0 : forall y:U, R x y -> Rplus x y + | Rplus_n : forall y z:U, R x y -> Rplus y z -> Rplus x z. Definition Strongly_confluent : Prop := forall x a b:U, R x a -> R x b -> ex (fun z:U => R a z /\ R b z). diff --git a/theories/Sets/Relations_3.v b/theories/Sets/Relations_3.v index d6202cffe..ec8fb7e6d 100755 --- a/theories/Sets/Relations_3.v +++ b/theories/Sets/Relations_3.v @@ -46,9 +46,9 @@ Section Relations_3. Definition Confluent : Prop := forall x:U, confluent x. - Inductive noetherian : U -> Prop := + Inductive noetherian (x: U) : Prop := definition_of_noetherian : - forall x:U, (forall y:U, R x y -> noetherian y) -> noetherian x. + (forall y:U, R x y -> noetherian y) -> noetherian x. Definition Noetherian : Prop := forall x:U, noetherian x. |