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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/RIneq.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/RIneq.v')
| -rw-r--r-- | theories/Reals/RIneq.v | 14 |
1 files changed, 14 insertions, 0 deletions
diff --git a/theories/Reals/RIneq.v b/theories/Reals/RIneq.v index 944e7da21..7cf372e63 100644 --- a/theories/Reals/RIneq.v +++ b/theories/Reals/RIneq.v @@ -1933,6 +1933,20 @@ Proof. apply (Rmult_le_compat_l x 0 y H H0). Qed. +Lemma Rle_Rinv : forall x y:R, 0 < x -> 0 < y -> x <= y -> / y <= / x. +Proof. + intros; apply Rmult_le_reg_l with x. + apply H. + rewrite <- Rinv_r_sym. + apply Rmult_le_reg_l with y. + apply H0. + rewrite Rmult_1_r; rewrite Rmult_comm; rewrite Rmult_assoc; + rewrite <- Rinv_l_sym. + rewrite Rmult_1_r; apply H1. + red in |- *; intro; rewrite H2 in H0; elim (Rlt_irrefl _ H0). + red in |- *; intro; rewrite H2 in H; elim (Rlt_irrefl _ H). +Qed. + Lemma double : forall r1, 2 * r1 = r1 + r1. Proof. intro; ring. |