Minor bugs fixes

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@8017 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 14 insertions, 11 deletions

diff --git a/contrib/recdef/Recdef.v b/contrib/recdef/Recdef.v
index 94315c08e9..2d206220e4 100644
--- a/contrib/recdef/Recdef.v
+++ b/contrib/recdef/Recdef.v
@@ -5,12 +5,8 @@
 (*    //   *      This file is distributed under the terms of the       *)
 (*         *       GNU Lesser General Public License Version 2.1        *)
 (************************************************************************)
-
-Require Import Arith.
-Require Import Compare_dec.
-Require Import Wf_nat.
-
-Declare ML Module "recdef".
+Require Compare_dec.
+Require Wf_nat.
 
 Section Iter.
 Variable A : Type.
@@ -24,22 +20,29 @@ Fixpoint iter (n : nat) : (A -> A) -> A -> A :=
 End Iter.
 
 Theorem SSplus_lt : forall p p' : nat, p < S (S (p + p')).
-auto with arith.
+  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.
 Qed.
  
+
 Theorem Splus_lt : forall p p' : nat, p' < S (p + p').
-auto with arith.
+  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.
 Qed.
 
 Theorem le_lt_SS : forall x y, x <= y -> x < S (S y).
-auto with arith.
+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.
 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 (le_gt_dec 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_le_weak; exact h].
+intros h; exists m; [apply le_n | apply Lt.lt_le_weak; exact h].
 Defined.