proposition: Theorem min_dec : ∀ n m, {min n m = n} + {min n m = m}.
proof: Proof. intros n m. destruct n as [n| ]; [ idtac | destruct m; right; reflexivity ]. destruct m as [m| ]; [ idtac | left; reflexivity ]. destruct (Nat.min_dec n m) as [H| H]. left; apply fin_inj_wd; assumption. right; apply fin_inj_wd; assumption. Qed.
imports: Utf8 Compare_dec NPeano Misc