proposition: Lemma merge2_add_edge (G: graph2) (r: equiv_rel G) x u y: merge2 (G ∔ [x, u, y]) r ≃2 merge2 G r ∔ [\pi x, u, \pi y].
proof: Proof. Iso2 (merge_add_edge _ _ _ _); by rewrite merge_add_edgeE. Defined.
imports: HB(structures) Coq(Setoid Morphisms) mathcomp(all_ssreflect) GraphTheory(edone finite_quotient preliminaries bij equiv) GraphTheory(setoid_bigop structures pttdom mgraph ptt)