proposition: Lemma reg_incl_sim : forall r1 r2, reg_incl r1 r2 && reg_incl r2 r1 = similar r1 r2.
proof: Proof. rewrite /reg_incl => r1 r2. apply/andP/idP. - case => h1 h2. transitivity (Plus r1 r2) => //. symmetry; by transitivity (Plus r2 r1). move => h; split. - transitivity (Plus r2 r2) => //. by apply similar_congr_Plus; last reflexivity. transitivity (Plus r1 r1) => //. by apply similar_congr_Plus; [symmetry | reflexivity]. Qed.
imports: Coq(RelationClasses Setoid Morphisms Permutation) Coq(SetoidList Mergesort Orders) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq fintype) mathcomp(bigop path) RegLang(languages) RegexpBrzozowski(glue gfinset regexp)