diff options
author | Maxime Dénès <mail@maximedenes.fr> | 2018-06-22 13:45:03 +0200 |
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committer | Maxime Dénès <mail@maximedenes.fr> | 2018-07-17 14:15:59 +0200 |
commit | 8c43e795c772090b336c0f170a6e5dcab196125d (patch) | |
tree | 98508f7e342142dd017da56872f74df73e6fce58 /plugins/micromega | |
parent | b799252775563b4f46f5ea39cbfc469759e7a296 (diff) |
Remove fourier plugin
As stated in the manual, the fourier tactic is subsumed by lra.
Diffstat (limited to 'plugins/micromega')
-rw-r--r-- | plugins/micromega/Fourier.v | 5 | ||||
-rw-r--r-- | plugins/micromega/Fourier_util.v | 31 |
2 files changed, 36 insertions, 0 deletions
diff --git a/plugins/micromega/Fourier.v b/plugins/micromega/Fourier.v new file mode 100644 index 000000000..0153de1da --- /dev/null +++ b/plugins/micromega/Fourier.v @@ -0,0 +1,5 @@ +Require Import Lra. +Require Export Fourier_util. + +#[deprecated(since = "8.9.0", note = "Use lra instead.")] +Ltac fourier := lra. diff --git a/plugins/micromega/Fourier_util.v b/plugins/micromega/Fourier_util.v new file mode 100644 index 000000000..b62153dee --- /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. |