diff options
Diffstat (limited to 'theories/Relations/Relation_Operators.v')
| -rw-r--r-- | theories/Relations/Relation_Operators.v | 18 |
1 files changed, 16 insertions, 2 deletions
diff --git a/theories/Relations/Relation_Operators.v b/theories/Relations/Relation_Operators.v index 701bc073..4e52017e 100644 --- a/theories/Relations/Relation_Operators.v +++ b/theories/Relations/Relation_Operators.v @@ -1,6 +1,6 @@ (************************************************************************) (* v * The Coq Proof Assistant / The Coq Development Team *) -(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014 *) +(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015 *) (* \VV/ **************************************************************) (* // * This file is distributed under the terms of the *) (* * GNU Lesser General Public License Version 2.1 *) @@ -46,6 +46,20 @@ Section Transitive_Closure. End Transitive_Closure. +(** ** Reflexive closure *) + +Section Reflexive_Closure. + Variable A : Type. + Variable R : relation A. + + (** Definition by direct transitive closure *) + + Inductive clos_refl (x: A) : A -> Prop := + | r_step (y:A) : R x y -> clos_refl x y + | r_refl : clos_refl x x. + +End Reflexive_Closure. + (** ** Reflexive-transitive closure *) Section Reflexive_Transitive_Closure. @@ -204,7 +218,7 @@ Section Lexicographic_Exponentiation. | d_nil : Desc Nil | d_one (x:A) : Desc (x :: Nil) | d_conc (x y:A) (l:List) : - leA x y -> Desc (l ++ y :: Nil) -> Desc ((l ++ y :: Nil) ++ x :: Nil). + clos_refl A leA x y -> Desc (l ++ y :: Nil) -> Desc ((l ++ y :: Nil) ++ x :: Nil). Definition Pow : Set := sig Desc. |