proposition: Lemma two_edges (a b c d: Lv) (u v: Le): edge_graph a u b ⊎ edge_graph c v d ≃ (two_graph a b ⊎ two_graph c d) ∔ [inl (inl tt), u, inl (inr tt)] ∔ [inr (inl tt), v, inr (inr tt)].
proof: Proof. etransitivity. apply (union_add_edge_l _ _ _ _). etransitivity. apply (add_edge_iso (union_add_edge_r _ _ _ _) _ _ _). apply add_edge_C. Defined.
imports: HB(structures) Coq(Setoid Morphisms) mathcomp(all_ssreflect) GraphTheory(edone finite_quotient preliminaries bij equiv) GraphTheory(setoid_bigop structures pttdom mgraph mgraph2 rewriting)