proposition: Lemma minus_lt : forall a b, a < b -> a - b = zero.
proof: Proof. induction 1;simpl. auto. generalize H;case a. case a';simpl;auto. intro H0;case (lt_irr H0). intros. rewrite (compare_rw1 H0). auto. case a. case (le_lt_dec n n'). auto. intro H0; absurd (n < n)%nat;auto with arith. eauto with arith. intros;rewrite (compare_rw2). case (lt_eq_lt_dec n n'). destruct s. auto. subst n';absurd (n < n)%nat;auto with arith. intro; absurd (n<n)%nat;eauto with arith. case a. case (le_lt_dec n n). auto. intro; absurd (n>n);auto with arith. intros; rewrite (compare_rw2). case (lt_eq_lt_dec n n). destruct s. auto. auto. intro; absurd (n < n)%nat;auto with arith. Qed.
imports: Arith Omega Compare_dec Relations Wellfounded Tools More_nat Wf_nat AccP not_decreasing ArithRing term rpo List