Library Coq.funind.Recdef

Require Compare_dec.
Require Wf_nat.

Section Iter.
Variable A : Type.

Fixpoint iter (n : nat) : (A -> A) -> A -> A :=
  fun (fl : A -> A) (def : A) =>
  match n with
  | O => def
  | S m => fl (iter m fl def)
  end.
End Iter.

Theorem SSplus_lt : forall p p' : nat, p < S (S (p + p')).

Theorem Splus_lt : forall p p' : nat, p' < S (p + p').

Theorem le_lt_SS : forall x y, x <= y -> x < S (S y).

Inductive max_type (m n:nat) : Set :=
  cmt : forall v, m <= v -> n <= v -> max_type m n.

Definition max : forall m n:nat, max_type m n.
Defined.