proposition: Lemma to_nat_minus : forall (x y:int), (x >= y) -> (y >= 0) -> to_nat (x - y) = (to_nat x - to_nat y)%nat :> nat.
proof: Proof. Proof using. intros. apply~ Z2Nat.inj_sub. Qed.
imports: Coq.ZArith.ZArith TLC(LibTactics LibLogic LibReflect LibRelation)