proposition: Theorem Qmin_comm : ∀ n m, Qmin n m == Qmin m n.
proof: Proof. intros n m. unfold Qmin. destruct (Qlt_le_dec n m) as [H₁| H₁]. destruct (Qlt_le_dec m n) as [H₂| H₂]; [ idtac | reflexivity ]. apply Qlt_le_weak, Qle_not_lt in H₂. contradiction. destruct (Qlt_le_dec m n) as [H₂| H₂]; [ reflexivity | idtac ]. apply Qle_antisym; assumption. Qed.
imports: Utf8 QArith NPeano Sorted Psatz