Module NdefOpsProp (Import N : NAxiomsRecSig').
Include NStrongRecProp N.
(** Nullity Test *)
Definition if_zero (A : Type) (a b : A) (n : N.t) : A :=
recursion a (fun _ _ => b) n.
Arguments if_zero [A] a b n.
Instance if_zero_wd (A : Type) :
Proper (Logic.eq ==> Logic.eq ==> N.eq ==> Logic.eq) (@if_zero A).

Theorem if_zero_succ :
forall (A : Type) (a b : A) (n : N.t), if_zero a b (S n) = b.