proposition: Lemma oiso2_add_test (F G : pre_graph) (i : F ⩭2 G) x a b : x \in vset F -> a ≡ b -> F[adt x <- a] ⩭2 G[adt i x <- b].
proof: Proof. case: i => isF isG i Vx ab. econstructor. apply: iso2_comp (iso2_sym _) _. by apply: pack_add_test. apply: iso2_comp. 2: apply: pack_add_test. 2: exact: (oiso2_vset (OIso2 i)). apply add_vlabel2_iso'' with i. 2:exact: ab. abstract (by rewrite /= vfun_bodyE /= pack_fsval pack_vE). Defined.
imports: Coq(Relation_Definitions Morphisms RelationClasses) mathcomp(all_ssreflect) GraphTheory(edone finite_quotient preliminaries bij equiv) GraphTheory(setoid_bigop structures pttdom mgraph mgraph2) GraphTheory(rewriting open_confluence finmap_plus)