proposition: Lemma connect_rev e : connect [rel x y | e y x] =2 [rel x y | connect e y x].
proof: Proof. suff crev e': subrel (connect [rel x y | e' y x]) [rel x y | connect e' y x]. by move=> x y; apply/idP/idP; apply: crev. move=> x y /connectP[p e_p p_y]; apply/connectP. exists (rev (belast x p)); first by rewrite p_y rev_path. by rewrite -(last_cons x) -rev_rcons p_y -lastI rev_cons last_rcons. Qed.
imports: mathcomp(ssreflect ssrbool ssrfun eqtype ssrnat) mathcomp(seq path fintype)