diff options
Diffstat (limited to 'theories/Reals/Rtrigo1.v')
-rw-r--r-- | theories/Reals/Rtrigo1.v | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/theories/Reals/Rtrigo1.v b/theories/Reals/Rtrigo1.v index 5f2e0d5b5..6b1754021 100644 --- a/theories/Reals/Rtrigo1.v +++ b/theories/Reals/Rtrigo1.v @@ -182,8 +182,8 @@ destruct (pre_cos_bound _ 0 lo up) as [_ upper]. apply Rle_lt_trans with (1 := upper). apply Rlt_le_trans with (2 := lower). unfold cos_approx, sin_approx. -simpl sum_f_R0; replace 7 with (IZR 7) by (simpl; field). -replace 8 with (IZR 8) by (simpl; field). +simpl sum_f_R0; change 7 with (IZR 7). +change 8 with (IZR 8). unfold cos_term, sin_term; simpl fact; rewrite !INR_IZR_INZ. simpl plus; simpl mult. field_simplify; @@ -1798,7 +1798,7 @@ Lemma cos_eq_0_0 (x:R) : Proof. rewrite cos_sin. intros Hx. destruct (sin_eq_0_0 (PI/2 + x) Hx) as (k,Hk). clear Hx. - exists (k-1)%Z. rewrite <- Z_R_minus; simpl. + exists (k-1)%Z. rewrite <- Z_R_minus; change (IZR 1) with 1. symmetry in Hk. field_simplify [Hk]. field. Qed. @@ -1836,7 +1836,7 @@ Proof. - right; left; auto. - left. clear Hi. subst. - replace 0 with (IZR 0 * PI) by (simpl; ring). f_equal. f_equal. + replace 0 with (IZR 0 * PI) by apply Rmult_0_l. f_equal. f_equal. apply one_IZR_lt1. split. + apply Rlt_le_trans with 0; |