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| author |  bertot <bertot@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-06-05 12:17:32 +0000 |
|---|---|---|
| committer | bertot <bertot@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2012-06-05 12:17:32 +0000 |
| commit | 9dea6a7404a251dbf7c467b445aca2686de59d22 (patch) | |
| tree | 765772817c26d94ed5af763cda7bc4ee763644b1 /theories/Reals/Rfunctions.v | |
| parent | 83b88cee6a66f999a4198200eade41ef49f038c6 (diff) | |
Modifications and rearrangements to remove the action that sin (PI/2) = 1
Beware that the definition of PI changes in the process
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@15425 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Rfunctions.v')
| -rw-r--r-- | theories/Reals/Rfunctions.v | 9 |
1 files changed, 9 insertions, 0 deletions
diff --git a/theories/Reals/Rfunctions.v b/theories/Reals/Rfunctions.v index c0cd78649..5ba0a187c 100644 --- a/theories/Reals/Rfunctions.v +++ b/theories/Reals/Rfunctions.v @@ -82,6 +82,15 @@ Proof. intros n0 H' m; rewrite H'; auto with real. Qed. +Lemma Rpow_mult_distr : forall (x y:R) (n:nat), (x * y) ^ n = x^n * y^n. +Proof. +intros x y n ; induction n. + field. + simpl. + repeat (rewrite Rmult_assoc) ; apply Rmult_eq_compat_l. + rewrite IHn ; field. +Qed. + Lemma pow_nonzero : forall (x:R) (n:nat), x <> 0 -> x ^ n <> 0. Proof. intro; simple induction n; simpl. |