Commit 95a6b1b3 authored by Guillaume Melquiond's avatar Guillaume Melquiond
Browse files

Simplified a bit.

parent c7dc30cc
Require Import Flocq_Raux. Require Import Flocq_Raux.
Require Import Flocq_defs. Require Import Flocq_defs.
Require Import Flocq_rnd_ex. Require Import Flocq_rnd_ex.
Require Import Flocq_float_prop.
Section RND_generic. Section RND_generic.
...@@ -37,8 +38,7 @@ intros x ((m,e),(H1,H2)). ...@@ -37,8 +38,7 @@ intros x ((m,e),(H1,H2)).
exists (Float beta (-m) e). exists (Float beta (-m) e).
split. split.
rewrite H1. rewrite H1.
unfold F2R. simpl. apply opp_F2R.
now rewrite opp_Z2R, Ropp_mult_distr_l_reverse.
intros H3. intros H3.
simpl in H2. simpl in H2.
assert (H4 := Ropp_neq_0_compat _ H3). assert (H4 := Ropp_neq_0_compat _ H3).
...@@ -342,8 +342,8 @@ rewrite Rmult_1_r. ...@@ -342,8 +342,8 @@ rewrite Rmult_1_r.
rewrite Ropp_mult_distr_l_reverse. rewrite Ropp_mult_distr_l_reverse.
rewrite <- epow_add. rewrite <- epow_add.
replace (ex - fexp ex + fexp ex)%Z with ex by ring. replace (ex - fexp ex + fexp ex)%Z with ex by ring.
rewrite <- (Ropp_involutive x). apply Ropp_le_cancel.
apply Ropp_le_contravar. rewrite Ropp_involutive.
now apply Rlt_le. now apply Rlt_le.
rewrite Z2R_IZR. rewrite Z2R_IZR.
exact (proj1 (archimed _)). exact (proj1 (archimed _)).
...@@ -519,9 +519,8 @@ apply lt_Z2R. ...@@ -519,9 +519,8 @@ apply lt_Z2R.
apply Rmult_lt_reg_r with (bpow ge). apply Rmult_lt_reg_r with (bpow ge).
apply epow_gt_0. apply epow_gt_0.
rewrite Rmult_0_l. rewrite Rmult_0_l.
rewrite opp_Z2R. change (0 < F2R (Float beta (-gm) ge))%R.
rewrite Ropp_mult_distr_l_reverse. rewrite <- opp_F2R.
unfold F2R in Hg1. simpl in Hg1.
rewrite <- Hg1. rewrite <- Hg1.
rewrite <- Ropp_0. rewrite <- Ropp_0.
now apply Ropp_lt_contravar. now apply Ropp_lt_contravar.
......
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