proposition: Lemma pIO_No x : x \notin pIO -> p_out G != x.
proof: Proof. apply: contraNneq => <-. by rewrite in_fset2 eqxx. Qed.
imports: HB(structures) Coq(Relation_Definitions Morphisms RelationClasses) mathcomp(all_ssreflect) GraphTheory(edone finite_quotient preliminaries bij equiv) GraphTheory(setoid_bigop structures pttdom rewriting) GraphTheory(finmap_plus)