*** empty log message ***

git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2270 85f007b7-540e-0410-9357-904b9bb8a0f7

1 files changed, 27 insertions, 0 deletions

diff --git a/theories/Reals/Rbase.v b/theories/Reals/Rbase.v
index 78e0876a0..45e03ca7a 100644
--- a/theories/Reals/Rbase.v
+++ b/theories/Reals/Rbase.v
@@ -1581,4 +1581,31 @@ end.
 
 Theorem INR_eq_INR2 : (n:nat) (INR n)==(INR2 n).
 Induction n; [Unfold INR INR2; Reflexivity | Intros; Unfold INR INR2; Fold INR INR2; Rewrite H; Case n0; [Reflexivity | Intros; Ring]].
+Save.
+
+(*****************************************************)
+(*          Some properties of Rmin and Rmax         *)
+(*****************************************************)
+Lemma Rmin_l : (x,y:R) ``(Rmin x y)<=x``.
+Intros; Unfold Rmin; Case (total_order_Rle x y); Intro H1; [Right; Reflexivity | Auto with real].
+Save.
+  
+Lemma Rmin_r : (x,y:R) ``(Rmin x y)<=y``.
+Intros; Unfold Rmin; Case (total_order_Rle x y); Intro H1; [Assumption | Auto with real].
+Save.
+
+Lemma Rmin_stable_in_posreal : (x,y:posreal) ``0<(Rmin x y)``.
+Intros; Apply Rmin_Rgt_r; Split; [Apply (cond_pos x) | Apply (cond_pos y)].
+Save.
+
+Lemma Rmax_l : (x,y:R) ``x<=(Rmax x y)``.
+Intros; Unfold Rmax; Case (total_order_Rle x y); Intro H1; [Assumption | Right; Reflexivity].
+Save.
+
+Lemma Rmax_r : (x,y:R) ``y<=(Rmax x y)``.
+Intros; Unfold Rmax; Case (total_order_Rle x y); Intro H1; [Right; Reflexivity | Auto with real].
+Save.
+
+Lemma Rmax_stable_in_negreal : (x,y:negreal) ``(Rmax x y)<0``.
+Intros; Unfold Rmax; Case (total_order_Rle x y); Intro; [Apply (cond_neg y) | Apply (cond_neg x)].
 Save.
\ No newline at end of file