The Coq Standard Library

# Library Coq.Wellfounded.Transitive_Closure

Author: Bruno Barras
Require Import Relation_Definitions.
Require Import Relation_Operators.
Section Wf_Transitive_Closure.
Variable A : Type.
Variable R : relation A.
Notation trans_clos := (clos_trans A R).
Lemma incl_clos_trans : inclusion A R trans_clos.
Lemma Acc_clos_trans : forall x:A, Acc R x -> Acc trans_clos x.
Hint Resolve Acc_clos_trans.
Lemma Acc_inv_trans : forall x y:A, trans_clos y x -> Acc R x -> Acc R y.
Theorem wf_clos_trans : well_founded R -> well_founded trans_clos.
End Wf_Transitive_Closure.