diff options
Diffstat (limited to 'theories/Reals/Rbasic_fun.v')
| -rw-r--r-- | theories/Reals/Rbasic_fun.v | 8 |
1 files changed, 5 insertions, 3 deletions
diff --git a/theories/Reals/Rbasic_fun.v b/theories/Reals/Rbasic_fun.v index 436a8011..0d1b06e2 100644 --- a/theories/Reals/Rbasic_fun.v +++ b/theories/Reals/Rbasic_fun.v @@ -6,7 +6,7 @@ (* * GNU Lesser General Public License Version 2.1 *) (************************************************************************) -(*i $Id: Rbasic_fun.v 5920 2004-07-16 20:01:26Z herbelin $ i*) +(*i $Id: Rbasic_fun.v 8838 2006-05-22 09:26:36Z herbelin $ i*) (*********************************************************) (** Complements for the real numbers *) @@ -107,11 +107,13 @@ Lemma RmaxLess2 : forall r1 r2, r2 <= Rmax r1 r2. intros r1 r2; unfold Rmax in |- *; case (Rle_dec r1 r2); auto with real. Qed. -Lemma RmaxSym : forall p q:R, Rmax p q = Rmax q p. +Lemma Rmax_comm : forall p q:R, Rmax p q = Rmax q p. intros p q; unfold Rmax in |- *; case (Rle_dec p q); case (Rle_dec q p); auto; intros H1 H2; apply Rle_antisym; auto with real. Qed. +Notation RmaxSym := Rmax_comm (only parsing). + Lemma RmaxRmult : forall (p q:R) r, 0 <= r -> Rmax (r * p) (r * q) = r * Rmax p q. intros p q r H; unfold Rmax in |- *. @@ -467,4 +469,4 @@ intros p0; apply Rabs_right; auto with real zarith. intros p0; rewrite Rabs_Ropp. apply Rabs_right; auto with real zarith. Qed. -
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