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| author |  Thomas Sibut-Pinote <thomas.sibut-pinote@inria.fr> | 2017-02-01 17:58:32 +0100 |
|---|---|---|
| committer | Thomas Sibut-Pinote <thomas.sibut-pinote@inria.fr> | 2017-02-15 17:56:14 +0100 |
| commit | f5c81ac1bcae7c40d5e89229647c06c97b5ddc85 (patch) | |
| tree | a5a2769d37103cdf9aff3314cc451b340b86ca18 /theories/Reals/Rpower.v | |
| parent | c17c3faee20251cd5c7168246e9ffcd12d557f85 (diff) | |
Added some theory on powerRZ.
For this, I used a new inductive type Z_spec to reason on Z.
Diffstat (limited to 'theories/Reals/Rpower.v')
| -rw-r--r-- | theories/Reals/Rpower.v | 14 |
1 files changed, 14 insertions, 0 deletions
diff --git a/theories/Reals/Rpower.v b/theories/Reals/Rpower.v index b3ce6fa33..93462a1fc 100644 --- a/theories/Reals/Rpower.v +++ b/theories/Reals/Rpower.v @@ -490,6 +490,20 @@ Proof. apply exp_Ropp. Qed. +Lemma powerRZ_Rpower x z : (0 < x)%R -> powerRZ x z = Rpower x (IZR z). +Proof. + intros Hx. + assert (x <> 0)%R + by now intros Habs; rewrite Habs in Hx; apply (Rlt_irrefl 0). + destruct (intP z). + - now rewrite Rpower_O. + - rewrite <- pow_powerRZ, <- Rpower_pow by assumption. + now rewrite INR_IZR_INZ. + - rewrite opp_IZR, Rpower_Ropp. + rewrite powerRZ_neg, powerRZ_inv by assumption. + now rewrite <- pow_powerRZ, <- INR_IZR_INZ, Rpower_pow. +Qed. + Theorem Rle_Rpower : forall e n m:R, 1 < e -> 0 <= n -> n <= m -> e ^R n <= e ^R m. Proof. |