proposition: Lemma abs_eq_succ_abs_minus_one : forall (x:int), x > 0 -> abs x = S (abs (x - 1)) :> nat.
proof: Proof. Proof using. intros. apply eq_nat_of_eq_int. rewrite abs_nonneg; try math. Qed.
imports: Coq.ZArith.ZArith TLC(LibTactics LibLogic LibReflect LibRelation)