diff options
Diffstat (limited to 'flocq/Prop/Fprop_relative.v')
| -rw-r--r-- | flocq/Prop/Fprop_relative.v | 13 |
1 files changed, 7 insertions, 6 deletions
diff --git a/flocq/Prop/Fprop_relative.v b/flocq/Prop/Fprop_relative.v index 585b71da..276ccd3b 100644 --- a/flocq/Prop/Fprop_relative.v +++ b/flocq/Prop/Fprop_relative.v @@ -44,7 +44,7 @@ Proof with auto with typeclass_instances. intros x b Hb0 Hxb. destruct (Req_dec x 0) as [Hx0|Hx0]. (* *) -exists R0. +exists 0%R. split. now rewrite Rabs_R0. rewrite Hx0, Rmult_0_l. @@ -71,7 +71,7 @@ Proof with auto with typeclass_instances. intros x b Hb0 Hxb. destruct (Req_dec x 0) as [Hx0|Hx0]. (* *) -exists R0. +exists 0%R. split. now rewrite Rabs_R0. rewrite Hx0, Rmult_0_l. @@ -588,7 +588,7 @@ rewrite Rabs_right;[assumption|apply Rle_ge; now left]. exists eps; exists 0%R. split;[assumption|split]. rewrite Rabs_R0; apply Rmult_le_pos. -auto with real. +apply Rlt_le, pos_half_prf. apply bpow_ge_0. split;[apply Rmult_0_r|idtac]. now rewrite Rplus_0_r. @@ -596,13 +596,14 @@ now rewrite Rplus_0_r. exists 0%R; exists (round beta (FLT_exp emin prec) (Znearest choice) x - x)%R. split. rewrite Rabs_R0; apply Rmult_le_pos. -auto with real. +apply Rlt_le, pos_half_prf. apply bpow_ge_0. split. apply Rle_trans with (/2*ulp beta (FLT_exp emin prec) x)%R. apply error_le_half_ulp. now apply FLT_exp_valid. -apply Rmult_le_compat_l; auto with real. +apply Rmult_le_compat_l. +apply Rlt_le, pos_half_prf. rewrite ulp_neq_0. 2: now apply Rgt_not_eq. apply bpow_le. @@ -650,7 +651,7 @@ destruct (Rtotal_order x 0) as [Nx|[Zx|Px]]. { apply (Rmult_le_reg_l 2 _ _ Rlt_0_2). rewrite Rmult_0_r, Rinv_r; [exact Rle_0_1|]. apply Rgt_not_eq, Rlt_gt, Rlt_0_2. } - exists R0; exists R0; rewrite Zx; split; [|split; [|split]]. + exists 0%R; exists 0%R; rewrite Zx; split; [|split; [|split]]. { now rewrite Rabs_R0; apply Rmult_le_pos; [|apply bpow_ge_0]. } { now rewrite Rabs_R0; apply Rmult_le_pos; [|apply bpow_ge_0]. } { now rewrite Rmult_0_l. } |