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+(************************************************************************)
+(*         *   The Coq Proof Assistant / The Coq Development Team       *)
+(*  v      *   INRIA, CNRS and contributors - Copyright 1999-2018       *)
+(* <O___,, *       (see CREDITS file for the list of authors)           *)
+(*   \VV/  **************************************************************)
+(*    //   *    This file is distributed under the terms of the         *)
+(*         *     GNU Lesser General Public License Version 2.1          *)
+(*         *     (see LICENSE file for the text of the license)         *)
+(************************************************************************)
+
+Require Export Coq.funind.FunInd.
+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).
+Proof.
+ intros. now apply Nat.lt_succ_r, Nat.le_le_succ_r.
+Qed.
+
+Theorem Splus_lt x y : y < S (x + y).
+Proof.
+ apply Nat.lt_succ_r. rewrite Nat.add_comm. apply Nat.le_add_r.
+Qed.
+
+Theorem SSplus_lt x y : x < S (S (x + y)).
+Proof.
+ apply le_lt_SS, Nat.le_add_r.
+Qed.
+
+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.
+Proof.
+ destruct (Compare_dec.le_gt_dec m n) as [h|h].
+ - exists n; [exact h | apply le_n].
+ - exists m; [apply le_n | apply Nat.lt_le_incl; exact h].
+Defined.
+
+Definition Acc_intro_generator_function := fun A R => @Acc_intro_generator A R 100.