intros n n1 n2 H' H'0; case (le_or_lt n1 n2); auto.
intros H'1; Contradict H'0; auto.
apply lt_not_le; auto with arith.
Qed.

Theorem min_n_0 : forall n : nat, min n 0 = 0.
intros n; case n; simpl in |- *; auto.