Section Induction.
Variable A : t -> Prop.
Hypothesis A_wd : Proper (eq ==> iff) A.
Hypothesis A0 : A 0.
Hypothesis AS : forall n, A n <-> A (S n).
(* Below, we use only -> direction *)
Let B (n : Z) := A (ZnZ.of_Z n).
End Induction.

Theorem sub_succ_r : forall n m, n - (S m) == P (n - m).