proposition: Lemma add_edge_edge G e e' x y x' y' u u' : e != e' -> G ∔ [e,x,u,y] ∔ [e',x',u',y'] ≡G G ∔ [e',x',u',y'] ∔ [e,x,u,y].
proof: Proof. move => eDe'. split => //=; first by rewrite fsetUA [[fset _;_]]fsetUC -fsetUA. 1: move => b. all: move => f; case/fset1UE => [->|[?]]; last case/fset1UE => [->|[? ?]]. all: by rewrite !updateE // eq_sym. 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)