proposition: Lemma freshP (E : {fset nat}) : fresh E \notin E.
proof: Proof. have S e' : e' \in E -> e' < fresh E. { rewrite /fresh ltnS => inE. by rewrite -[e']/(val [`inE]) leq_bigmax. } apply/negP => /S. by rewrite ltnn. 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)