Library Coq.funind.Recdef


Require Import PeanoNat.

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

Theorem Splus_lt x y : y < S (x + y).

Theorem SSplus_lt x y : x < S (S (x + y)).

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

Definition max m n : max_type m n.

Definition Acc_intro_generator_function := fun A R => @Acc_intro_generator A R 100.