proposition: Lemma add_vlabel_edge a u b (x: unit+unit) c: edge_graph a u b [tst x <- c] ≃ edge_graph (if x then a⊗c else a) u (if x then b else b⊗c).
proof: Proof. etransitivity. apply iso_sym. apply add_edge_vlabel. etransitivity. apply (add_edge_iso (add_vlabel_two a b x c)). by case x; case. Defined.
imports: Coq(Morphisms RelationClasses) mathcomp(all_ssreflect) GraphTheory(edone finite_quotient preliminaries bij) GraphTheory(equiv digraph setoid_bigop structures)