proposition: Lemma lt_not_gt : forall a b, a < b -> ~ (b < a).
proof: Proof. intros a b H H0. case (lt_irr (alpha := a));auto. apply transitivity with b;auto. Qed.
imports: EPSILON0 Arith List Omega Compare_dec Relations Wellfounded Max Tools More_nat AccP not_decreasing EPSILON0 More_nat Gamma0_prelude Gamma0_length term rpo