proposition: Lemma oarc_add_edge (G : pre_graph) e e' x y x' y' u u' : e' != e -> oarc G e' x' u' y' -> oarc (G ∔ [e,x,u,y]) e' x' u' y'.
proof: Proof. move => eDe'. rewrite /oarc /= !updateE // in_fset1U (negbTE eDe') /=. case => A [b] B. split => //. exists b. by rewrite !updateE. 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)