proposition: Lemma add_edge_vseparator (G : sgraph) (x y : G) (S : {set G}) : x \in S -> y \in S -> vseparator G S -> vseparator (add_edge x y) S.
proof: Proof. move => xS yS /vseparator_separation [V1 [V2 [psepV ?]]]; subst S. by apply: proper_vseparator; exact: add_edge_proper_separation. Qed.
imports: mathcomp(all_ssreflect) GraphTheory(edone preliminaries digraph mgraph sgraph set_tac)