proposition: Lemma remove_edgeK (G : pre_graph) (isG : is_graph G) e x y u : is_edge G e x u y -> (G - [fset e]) ∔ [e,x,u,y] ≡G G.
proof: Proof. case => E [A B C]. split => //=. - by rewrite fsetD1K. - move => b. rewrite fsetD1K // => e'. case: (altP (e' =P e)) => [->|?] ?; rewrite updateE //. by case: b; rewrite ?A ?B. - move => e'. rewrite fsetD1K // => He'. by case: (altP (e' =P e)) => [->|?]; rewrite updateE // C. 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)