proposition: Lemma separates_sym x y S : separates x y S <-> separates y x S.
proof: Proof. suff X u v: separates u v S -> separates v u S by split; exact: X. move => [uNS vNS P]; split => // p; have [z] := P (prev p). by rewrite mem_prev; exists z. Qed.
imports: mathcomp(all_ssreflect) GraphTheory(edone preliminaries digraph mgraph sgraph set_tac)