diff options
author | Benjamin Barenblat <bbaren@debian.org> | 2019-02-02 19:29:23 -0500 |
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committer | Benjamin Barenblat <bbaren@debian.org> | 2019-02-02 19:29:23 -0500 |
commit | 9ebf44d84754adc5b64fcf612c6816c02c80462d (patch) | |
tree | bf5e06a28488e0e06a2f2011ff0d110e2e02f8fc /plugins/micromega/Fourier_util.v | |
parent | 9043add656177eeac1491a73d2f3ab92bec0013c (diff) |
Imported Upstream version 8.9.0upstream/8.9.0upstream
Diffstat (limited to 'plugins/micromega/Fourier_util.v')
-rw-r--r-- | plugins/micromega/Fourier_util.v | 31 |
1 files changed, 31 insertions, 0 deletions
diff --git a/plugins/micromega/Fourier_util.v b/plugins/micromega/Fourier_util.v new file mode 100644 index 00000000..b62153de --- /dev/null +++ b/plugins/micromega/Fourier_util.v @@ -0,0 +1,31 @@ +Require Export Rbase. +Require Import Lra. + +Open Scope R_scope. + +Lemma Rlt_mult_inv_pos : forall x y:R, 0 < x -> 0 < y -> 0 < x * / y. +intros x y H H0; try assumption. +replace 0 with (x * 0). +apply Rmult_lt_compat_l; auto with real. +ring. +Qed. + +Lemma Rlt_zero_pos_plus1 : forall x:R, 0 < x -> 0 < 1 + x. +intros x H; try assumption. +rewrite Rplus_comm. +apply Rle_lt_0_plus_1. +red; auto with real. +Qed. + +Lemma Rle_zero_pos_plus1 : forall x:R, 0 <= x -> 0 <= 1 + x. + intros; lra. +Qed. + +Lemma Rle_mult_inv_pos : forall x y:R, 0 <= x -> 0 < y -> 0 <= x * / y. +intros x y H H0; try assumption. +case H; intros. +red; left. +apply Rlt_mult_inv_pos; auto with real. +rewrite <- H1. +red; right; ring. +Qed. |