Uniformisation (Qed/Save et Implicits Arguments)

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2650 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 15 insertions, 15 deletions

diff --git a/theories/Num/LeProps.v b/theories/Num/LeProps.v
index bf7af0d66..9703ec77f 100644
--- a/theories/Num/LeProps.v
+++ b/theories/Num/LeProps.v
@@ -13,18 +13,18 @@ Require Export LeAxioms.
 
 Lemma lt_le : (x,y:N)(x<y)->(x<=y).
 Auto with num.
-Save.
+Qed.
 
 Lemma eq_le : (x,y:N)(x=y)->(x<=y).
 Auto with num.
-Save.
+Qed.
 
 (** compatibility with equality *)
 Lemma le_eq_compat : (x1,x2,y1,y2:N)(x1=y1)->(x2=y2)->(x1<=x2)->(y1<=y2).
 Intros x1 x2 y1 y2 eq1 eq2 le1; Case le_lt_or_eq with 1:=le1; Intro.
 EAuto with num.
 Apply eq_le; Apply eq_trans with x1; EAuto with num.
-Save.
+Qed.
 Hints Resolve le_eq_compat : num.
 
 (** Transitivity *)
@@ -33,31 +33,31 @@ Intros x y z le1 le2.
 Case le_lt_or_eq with 1:=le1; Intro.
 Case le_lt_or_eq with 1:=le2; EAuto with num.
 EAuto with num.
-Save.
+Qed.
 Hints Resolve le_trans : num.
 
 (** compatibility with equality, addition and successor *)
 Lemma le_add_compat_l : (x,y,z:N)(x<=y)->((x+z)<=(y+z)).
 Intros x y z le1.
 Case le_lt_or_eq with 1:=le1; EAuto with num.
-Save.
+Qed.
 Hints Resolve le_add_compat_l : num.
 
 Lemma le_add_compat_r : (x,y,z:N)(x<=y)->((z+x)<=(z+y)).
 Intros x y z H; Apply le_eq_compat with (x+z) (y+z); Auto with num.
-Save.
+Qed.
 Hints Resolve le_add_compat_r : num.
 
 Lemma le_add_compat : (x1,x2,y1,y2:N)(x1<=x2)->(y1<=y2)->((x1+y1)<=(x2+y2)).
 Intros; Apply le_trans with (x1+y2); Auto with num.
-Save.
+Qed.
 Hints Immediate le_add_compat : num.
 
 (* compatibility with successor *)
 Lemma le_S_compat : (x,y:N)(x<=y)->((S x)<=(S y)).
 Intros x y le1.
 Case le_lt_or_eq with 1:=le1; EAuto with num.
-Save.
+Qed.
 Hints Resolve le_S_compat : num.
 
 
@@ -65,39 +65,39 @@ Hints Resolve le_S_compat : num.
 Lemma le_lt_x_Sy : (x,y:N)(x<=y)->(x<(S y)).
 Intros x y le1.
 Case le_lt_or_eq with 1:=le1; Auto with num.
-Save.
+Qed.
 Hints Immediate le_lt_x_Sy : num.
 
 Lemma le_le_x_Sy : (x,y:N)(x<=y)->(x<=(S y)).
 Auto with num.
-Save.
+Qed.
 Hints Immediate le_le_x_Sy : num.
 
 Lemma le_Sx_y_lt : (x,y:N)((S x)<=y)->(x<y).
 Intros x y le1.
 Case le_lt_or_eq with 1:=le1; EAuto with num.
-Save.
+Qed.
 Hints Immediate le_Sx_y_lt : num.
 
 (** Combined transitivity *)
 Lemma lt_le_trans : (x,y,z:N)(x<y)->(y<=z)->(x<z).
 Intros x y z lt1 le1; Case le_lt_or_eq with 1:= le1; EAuto with num.
-Save.
+Qed.
 
 Lemma le_lt_trans : (x,y,z:N)(x<=y)->(y<z)->(x<z).
 Intros x y z le1 lt1; Case le_lt_or_eq with 1:= le1; EAuto with num.
-Save.
+Qed.
 Hints Immediate lt_le_trans le_lt_trans : num.
 
 (** weaker compatibility results involving [<] and [<=] *)
 Lemma lt_add_compat_weak_l : (x1,x2,y1,y2:N)(x1<=x2)->(y1<y2)->((x1+y1)<(x2+y2)).
 Intros; Apply lt_le_trans with (x1+y2); Auto with num.
-Save.
+Qed.
 Hints Immediate  lt_add_compat_weak_l : num.
 
 Lemma lt_add_compat_weak_r : (x1,x2,y1,y2:N)(x1<x2)->(y1<=y2)->((x1+y1)<(x2+y2)).
 Intros; Apply le_lt_trans with (x1+y2); Auto with num.
-Save.
+Qed.
 Hints Immediate lt_add_compat_weak_r : num.