diff options
Diffstat (limited to 'theories/Relations')
| -rw-r--r-- | theories/Relations/Operators_Properties.v | 8 | ||||
| -rw-r--r-- | theories/Relations/Relation_Operators.v | 14 | ||||
| -rw-r--r-- | theories/Relations/Relations.v | 6 |
3 files changed, 14 insertions, 14 deletions
diff --git a/theories/Relations/Operators_Properties.v b/theories/Relations/Operators_Properties.v index 40fd8f36..7e202359 100644 --- a/theories/Relations/Operators_Properties.v +++ b/theories/Relations/Operators_Properties.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Operators_Properties.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: Operators_Properties.v 9597 2007-02-06 19:44:05Z herbelin $ i*) (****************************************************************************) (* Bruno Barras *) @@ -18,7 +18,7 @@ Require Import Relation_Operators. Section Properties. - Variable A : Set. + Variable A : Type. Variable R : relation A. Let incl (R1 R2:relation A) : Prop := forall x y:A, R1 x y -> R2 x y. @@ -43,7 +43,7 @@ Section Properties. Qed. Lemma clos_refl_trans_ind_left : - forall (A:Set) (R:A -> A -> Prop) (M:A) (P:A -> Prop), + forall (A:Type) (R:A -> A -> Prop) (M:A) (P:A -> Prop), P M -> (forall P0 N:A, clos_refl_trans A R M P0 -> P P0 -> R P0 N -> P N) -> forall a:A, clos_refl_trans A R M a -> P a. @@ -95,4 +95,4 @@ Section Properties. End Clos_Refl_Sym_Trans. -End Properties.
\ No newline at end of file +End Properties. diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v index 089246da..4c5a6519 100644 --- a/theories/Relations/Relation_Operators.v +++ b/theories/Relations/Relation_Operators.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Relation_Operators.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: Relation_Operators.v 9610 2007-02-07 14:45:18Z herbelin $ i*) (****************************************************************************) (* Bruno Barras, Cristina Cornes *) @@ -78,7 +78,7 @@ End Union. Section Disjoint_Union. -Variables A B : Set. +Variables A B : Type. Variable leA : A -> A -> Prop. Variable leB : B -> B -> Prop. @@ -94,8 +94,8 @@ End Disjoint_Union. Section Lexicographic_Product. (* Lexicographic order on dependent pairs *) - Variable A : Set. - Variable B : A -> Set. + Variable A : Type. + Variable B : A -> Type. Variable leA : A -> A -> Prop. Variable leB : forall x:A, B x -> B x -> Prop. @@ -110,8 +110,8 @@ End Lexicographic_Product. Section Symmetric_Product. - Variable A : Set. - Variable B : Set. + Variable A : Type. + Variable B : Type. Variable leA : A -> A -> Prop. Variable leB : B -> B -> Prop. @@ -125,7 +125,7 @@ End Symmetric_Product. Section Swap. - Variable A : Set. + Variable A : Type. Variable R : A -> A -> Prop. Inductive swapprod : A * A -> A * A -> Prop := diff --git a/theories/Relations/Relations.v b/theories/Relations/Relations.v index 9b2f4057..9da30e9b 100644 --- a/theories/Relations/Relations.v +++ b/theories/Relations/Relations.v @@ -6,14 +6,14 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Relations.v 9245 2006-10-17 12:53:34Z notin $ i*) +(*i $Id: Relations.v 9597 2007-02-06 19:44:05Z herbelin $ i*) Require Export Relation_Definitions. Require Export Relation_Operators. Require Export Operators_Properties. Lemma inverse_image_of_equivalence : - forall (A B:Set) (f:A -> B) (r:relation B), + forall (A B:Type) (f:A -> B) (r:relation B), equivalence B r -> equivalence A (fun x y:A => r (f x) (f y)). Proof. intros; split; elim H; red in |- *; auto. @@ -21,7 +21,7 @@ Proof. Qed. Lemma inverse_image_of_eq : - forall (A B:Set) (f:A -> B), equivalence A (fun x y:A => f x = f y). + forall (A B:Type) (f:A -> B), equivalence A (fun x y:A => f x = f y). Proof. split; red in |- *; [ (* reflexivity *) reflexivity |