diff options
author | delahaye <delahaye@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-03-17 07:25:23 +0000 |
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committer | delahaye <delahaye@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2002-03-17 07:25:23 +0000 |
commit | d440c9c6b4c64bfea5e1dc6bc4003d677fd493ca (patch) | |
tree | 19225b9e815613bf1cdf5982c4d9b09d9e1c51d7 /theories/Reals | |
parent | 1a750105e7d9630acf44dd0833cdc34578a0aea5 (diff) |
Field ne fait maintenant que les reductions necessaires
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@2539 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals')
-rw-r--r-- | theories/Reals/Ranalysis.v | 4 | ||||
-rw-r--r-- | theories/Reals/Rlimit.v | 6 | ||||
-rw-r--r-- | theories/Reals/Rtrigo.v | 2 |
3 files changed, 6 insertions, 6 deletions
diff --git a/theories/Reals/Ranalysis.v b/theories/Reals/Ranalysis.v index 005bdb3a1..dcf4e6406 100644 --- a/theories/Reals/Ranalysis.v +++ b/theories/Reals/Ranalysis.v @@ -750,7 +750,7 @@ Field. DiscrR. Case delta; Intros. Apply prod_neq_R0. -Red; Intro H13; Rewrite H13 in cond_pos; Elim (Rlt_antirefl ``0`` cond_pos). +Compute; Intro H13; Rewrite H13 in cond_pos; Elim (Rlt_antirefl ``0`` cond_pos). Apply Rinv_neq_R0; DiscrR. Replace ``((f (x+delta/2))-(f x))/(delta/2)`` with ``-(((f x)-(f (x+delta/2)))/(delta/2))``. Rewrite <- Ropp_O. @@ -765,7 +765,7 @@ Left; Apply Rlt_Rinv; Assumption. Field. Case delta; Intros. Apply prod_neq_R0. -Red; Intro H13; Rewrite H13 in cond_pos; Elim (Rlt_antirefl ``0`` cond_pos). +Compute; Intro H13; Rewrite H13 in cond_pos; Elim (Rlt_antirefl ``0`` cond_pos). Apply Rinv_neq_R0; DiscrR. Split. Unfold Rdiv; Apply prod_neq_R0. diff --git a/theories/Reals/Rlimit.v b/theories/Reals/Rlimit.v index 0c1ad9305..f31429d4a 100644 --- a/theories/Reals/Rlimit.v +++ b/theories/Reals/Rlimit.v @@ -618,8 +618,8 @@ Apply Rlt_Rinv; Cut ~(O=(2)); [Intro H17; Generalize (lt_INR_0 (2) (neq_O_lt (2) Replace ``(Rabsolu (f x))*(Rabsolu l)*/2*/(Rabsolu (f x))`` with ``(Rabsolu l)/2``. Replace ``(Rabsolu (f x))*(Rabsolu l)*/2*(2*/(Rabsolu l))`` with ``(Rabsolu (f x))``. Assumption. -Field; Apply prod_neq_R0; [DiscrR | Case (case_Rabsolu l); Intro; [Apply Ropp_neq; Assumption | Assumption]]. -Unfold Rdiv; Field; Apply prod_neq_R0; [DiscrR | Case (case_Rabsolu (f x)); Intro; [Apply Ropp_neq; Assumption | Assumption]]. +Field; Apply prod_neq_R0; [DiscrR | Unfold Rabsolu; Case (case_Rabsolu l); Intro; [Apply Ropp_neq; Assumption | Assumption]]. +Unfold Rdiv; Field; Apply prod_neq_R0; [DiscrR | Unfold Rabsolu; Case (case_Rabsolu (f x)); Intro; [Apply Ropp_neq; Assumption | Assumption]]. Apply Rabsolu_no_R0; Assumption. Apply Rabsolu_no_R0; Assumption. Apply Rabsolu_no_R0; Assumption. @@ -631,7 +631,7 @@ Intro; Elim (Rlt_antirefl ``0`` (Rlt_trans ``0`` ``(Rabsolu l)/2`` ``0`` H17 H15 Unfold Rdiv; Apply Rmult_lt_pos. Apply Rabsolu_pos_lt; Assumption. Apply Rlt_Rinv; Cut ~(O=(2)); [Intro H17; Generalize (lt_INR_0 (2) (neq_O_lt (2) H17)); Unfold INR; Intro; Assumption | Discriminate]. -Unfold Rdiv; Field; DiscrR. +Field; DiscrR. Split; [Assumption | Apply Rlt_le_trans with (Rmin delta1 delta2); [Assumption | Apply Rmin_r]]. Split; [Assumption | Apply Rlt_le_trans with (Rmin delta1 delta2); [Assumption | Apply Rmin_l]]. Change ``0<eps*(Rsqr l)/2``; Unfold Rdiv; Repeat Rewrite Rmult_assoc; Repeat Apply Rmult_lt_pos. diff --git a/theories/Reals/Rtrigo.v b/theories/Reals/Rtrigo.v index 1115ec19f..d1fc539f8 100644 --- a/theories/Reals/Rtrigo.v +++ b/theories/Reals/Rtrigo.v @@ -264,7 +264,7 @@ Intros; Elim (sin_eq_0 x); Intros; Apply (H1 H). Save. Lemma cos_eq_0_0 : (x:R) (cos x)==R0 -> (EXT k : Z | ``x==(IZR k)*PI+PI/2``). -Intros x H; Rewrite -> cos_sin in H; Generalize (sin_eq_0_0 (Rplus (Rdiv PI (INR (2))) x) H); Intro H2; Elim H2; Intros x0 H3; Exists (Zminus x0 (inject_nat (S O))); Rewrite <- Z_R_minus; Ring; Rewrite Rmult_sym; Rewrite <- H3; Field; DiscrR. +Intros x H; Rewrite -> cos_sin in H; Generalize (sin_eq_0_0 (Rplus (Rdiv PI (INR (2))) x) H); Intro H2; Elim H2; Intros x0 H3; Exists (Zminus x0 (inject_nat (S O))); Rewrite <- Z_R_minus; Ring; Rewrite Rmult_sym; Rewrite <- H3; Unfold INR; Field; DiscrR. Save. Lemma cos_eq_0_1 : (x:R) (EXT k : Z | ``x==(IZR k)*PI+PI/2``) -> ``(cos x)==0``. |