proposition: Theorem nlt_ge : ∀ n m, ¬(n < m) ↔ m ≤ n.
proof: Proof. intros n m. split; intros H. destruct n as [n| ]; [ idtac | constructor ]. destruct m as [m| ]. apply fin_le_mono, Nat.nlt_ge. intros I; apply H. apply fin_lt_mono; assumption. exfalso; apply H; constructor. destruct n as [n| ]. destruct m as [m| ]; [ idtac | inversion H ]. apply fin_le_mono, Nat.nlt_ge in H. intros I; apply H. apply fin_lt_mono; assumption. destruct m; intros I; inversion I. Qed.
imports: Utf8 Compare_dec NPeano Misc