proposition: Lemma fin__nat : forall (n : nat) (m : nat) (p : m < n), fin_to_nat (nat_to_fin m p) = m.
proof: Proof. intros. funelim (nat_to_fin m p); simp fin_to_nat. reflexivity. simpl. now rewrite H. Qed.
imports: Program Equations.Prop.EqDecInstances Equations.Prop.Equations