proposition: Lemma trans_lexico3 : forall A1 A2 A3 (R1:binary A1) (R2:binary A2) (R3:binary A3), trans R1 -> trans R2 -> trans R3 -> trans (lexico3 R1 R2 R3).
proof: Proof. Proof using. introv Tr1 Tr2 Tr3. applys~ trans_lexico2. applys~ trans_lexico2. Qed.
imports: TLC(LibTactics LibLogic LibBool LibLogic LibProd LibSum)