proposition: Lemma semiconn_lex : forall x y, x != y -> lex x y || lex y x.
proof: Proof. move=>[x1 x2][y1 y2]; rewrite /lex /=. by case: ifP=>H1 H2; rewrite eq_sym H1 semiconnex //; move: H2; rewrite -pair_eqE /= H1 //. Qed.
imports: Coq(ssreflect ssrbool ssrfun) mathcomp(ssrnat eqtype seq path fintype) pcm(options)