diff options
Diffstat (limited to 'theories')
| -rw-r--r-- | theories/Numbers/Cyclic/Int63/Int63.v | 10 | ||||
| -rw-r--r-- | theories/Reals/Rtrigo_calc.v | 8 |
2 files changed, 7 insertions, 11 deletions
diff --git a/theories/Numbers/Cyclic/Int63/Int63.v b/theories/Numbers/Cyclic/Int63/Int63.v index 9bb16b97e2..c81ba02230 100644 --- a/theories/Numbers/Cyclic/Int63/Int63.v +++ b/theories/Numbers/Cyclic/Int63/Int63.v @@ -812,14 +812,6 @@ Proof. eapply Z.lt_le_trans; [ | apply Zpower2_le_lin ]; auto with zarith. Qed. -Lemma lsr_add_distr x y n: (x + y) << n = ((x << n) + (y << n))%int63. -Proof. - apply to_Z_inj. - rewrite -> add_spec, !lsl_spec, add_spec. - rewrite -> Zmult_mod_idemp_l, <-Zplus_mod. - apply f_equal2 with (f := Zmod); auto with zarith. -Qed. - (* LSL *) Lemma lsl0 i: 0 << i = 0%int63. Proof. @@ -1119,7 +1111,7 @@ Proof. generalize (add_le_r x y); rewrite Heq, lor_le; intro Hb. generalize Heq; rewrite (bit_split x) at 1; rewrite (bit_split y )at 1; clear Heq. rewrite (fun y => add_comm y (bit x 0)), <-!add_assoc, add_comm, - <-!add_assoc, (add_comm (bit y 0)), add_assoc, <-lsr_add_distr. + <-!add_assoc, (add_comm (bit y 0)), add_assoc, <-lsl_add_distr. rewrite (bit_split (x lor y)), lor_spec. intros Heq. assert (F: (bit x 0 + bit y 0)%int63 = (bit x 0 || bit y 0)). diff --git a/theories/Reals/Rtrigo_calc.v b/theories/Reals/Rtrigo_calc.v index 5ed60b0a0f..2428fc495d 100644 --- a/theories/Reals/Rtrigo_calc.v +++ b/theories/Reals/Rtrigo_calc.v @@ -178,7 +178,7 @@ Proof. change (cos (PI / 4) <> 0); rewrite cos_PI4; apply R1_sqrt2_neq_0. Qed. -Lemma cos3PI4 : cos (3 * (PI / 4)) = -1 / sqrt 2. +Lemma cos_3PI4 : cos (3 * (PI / 4)) = -1 / sqrt 2. Proof. replace (3 * (PI / 4)) with (PI / 2 - - (PI / 4)) by field. rewrite cos_shift; rewrite sin_neg; rewrite sin_PI4. @@ -186,12 +186,16 @@ Proof. ring. Qed. -Lemma sin3PI4 : sin (3 * (PI / 4)) = 1 / sqrt 2. +#[deprecated(since="8.10",note="Use cos_3PI4 instead.")] Notation cos3PI4 := cos_3PI4. + +Lemma sin_3PI4 : sin (3 * (PI / 4)) = 1 / sqrt 2. Proof. replace (3 * (PI / 4)) with (PI / 2 - - (PI / 4)) by field. now rewrite sin_shift, cos_neg, cos_PI4. Qed. +#[deprecated(since="8.10",note="Use sin_3PI4 instead.")] Notation sin3PI4 := sin_3PI4. + Lemma cos_PI6 : cos (PI / 6) = sqrt 3 / 2. Proof with trivial. apply Rsqr_inj... |