From 7cfc4e5146be5666419451bdd516f1f3f264d24a Mon Sep 17 00:00:00 2001
From: Enrico Tassi <gareuselesinge@debian.org>
Date: Sun, 25 Jan 2015 14:42:51 +0100
Subject: Imported Upstream version 8.5~beta1+dfsg

---
 plugins/funind/Recdef.v | 38 ++++++++++++++++++++------------------
 1 file changed, 20 insertions(+), 18 deletions(-)

(limited to 'plugins/funind/Recdef.v')

diff --git a/plugins/funind/Recdef.v b/plugins/funind/Recdef.v
index 51ede26e..a63941f0 100644
--- a/plugins/funind/Recdef.v
+++ b/plugins/funind/Recdef.v
@@ -1,10 +1,13 @@
 (************************************************************************)
 (*  v      *   The Coq Proof Assistant  /  The Coq Development Team     *)
-(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2014     *)
+(* <O___,, *   INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2015     *)
 (*   \VV/  **************************************************************)
 (*    //   *      This file is distributed under the terms of the       *)
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
+
+Require Import PeanoNat.
+
 Require Compare_dec.
 Require Wf_nat.
 
@@ -19,30 +22,29 @@ Fixpoint iter (n : nat) : (A -> A) -> A -> A :=
   end.
 End Iter.
 
-Theorem SSplus_lt : forall p p' : nat, p < S (S (p + p')).
-  intro p; intro p'; change (S p <= S (S (p + p')));
-    apply le_S; apply Gt.gt_le_S; change (p < S (p + p'));
-    apply Lt.le_lt_n_Sm; apply Plus.le_plus_l.
+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 : forall p p' : nat, p' < S (p + p').
-  intro p; intro p'; change (S p' <= S (p + p'));
-    apply Gt.gt_le_S; change (p' < S (p + p')); apply Lt.le_lt_n_Sm;
-       apply Plus.le_plus_r.
+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 le_lt_SS : forall x y, x <= y -> x < S (S y).
-intro x; intro y; intro H; change (S x <= S (S y));
-    apply le_S; apply Gt.gt_le_S; change (x < S y);
-    apply Lt.le_lt_n_Sm; exact H.
+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 : forall m n:nat, max_type m n.
-intros m n; case (Compare_dec.le_gt_dec m n).
-intros h; exists n; [exact h | apply le_n].
-intros h; exists m; [apply le_n | apply Lt.lt_le_weak; exact h].
+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.
-- 
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