diff options
| author |  desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-15 15:35:04 +0000 |
|---|---|---|
| committer | desmettr <desmettr@85f007b7-540e-0410-9357-904b9bb8a0f7> | 2003-01-15 15:35:04 +0000 |
| commit | fea0a3265a7191a7e8c13028e7edd9bf29ba4d25 (patch) | |
| tree | f0993cfb172fd6e3cd280fcebf61ac0d6dc3e71b /theories/Reals/Ranalysis2.v | |
| parent | d72eb6e333f710bb8f4ea0061e8399aafba19fe0 (diff) | |
Nouvelle interprétation des nombres réels
git-svn-id: svn+ssh://scm.gforge.inria.fr/svn/coq/trunk@3499 85f007b7-540e-0410-9357-904b9bb8a0f7
Diffstat (limited to 'theories/Reals/Ranalysis2.v')
| -rw-r--r-- | theories/Reals/Ranalysis2.v | 18 |
1 files changed, 12 insertions, 6 deletions
diff --git a/theories/Reals/Ranalysis2.v b/theories/Reals/Ranalysis2.v index 85c92176f..5af07f40f 100644 --- a/theories/Reals/Ranalysis2.v +++ b/theories/Reals/Ranalysis2.v @@ -34,11 +34,11 @@ Case (total_order_Rle x y); Intro; Assumption. Qed. Lemma Rgt_8_0 : ``0 < 8``. -Cut ~(O=(8)); [Intro H; Generalize (lt_INR_0 (8) (neq_O_lt (8) H)); Rewrite INR_eq_INR2; Unfold INR2; Intro H0; Assumption | Discriminate]. +Sup0. Qed. Lemma Rgt_4_0 : ``0 < 4``. -Cut ~(O=(4)); [Intro H; Generalize (lt_INR_0 (4) (neq_O_lt (4) H)); Rewrite INR_eq_INR2; Unfold INR2; Intro H0; Assumption | Discriminate]. +Sup0. Qed. Lemma maj_term1 : (x,h,eps,l1,alp_f2:R;eps_f2,alp_f1d:posreal;f1,f2:R->R) ``0 < eps`` -> ``(f2 x)<>0`` -> ``(f2 (x+h))<>0`` -> ((h:R)``h <> 0``->``(Rabsolu h) < alp_f1d``->``(Rabsolu (((f1 (x+h))-(f1 x))/h-l1)) < (Rabsolu ((eps*(f2 x))/8))``) -> ((a:R)``(Rabsolu a) < (Rmin eps_f2 alp_f2)``->``/(Rabsolu (f2 (x+a))) < 2/(Rabsolu (f2 x))``) -> ``h<>0`` -> ``(Rabsolu h)<alp_f1d`` -> ``(Rabsolu h) < (Rmin eps_f2 alp_f2)`` -> ``(Rabsolu (/(f2 (x+h))*(((f1 (x+h))-(f1 x))/h-l1))) < eps/4``. @@ -98,7 +98,8 @@ Unfold Rdiv in H8; Exact H8. Symmetry; Apply Rabsolu_right; Left; Sup0. Right. Unfold Rsqr Rdiv. -Repeat Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Do 1 Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Do 1 Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. Repeat Rewrite Rabsolu_mult. Repeat Rewrite Rabsolu_Rinv; Try Assumption Orelse DiscrR. Replace (Rabsolu eps) with eps. @@ -144,7 +145,8 @@ Unfold Rdiv in H9; Exact H9. Symmetry; Apply Rabsolu_right; Left; Sup0. Right. Unfold Rsqr Rdiv. -Repeat Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. Repeat Rewrite Rabsolu_mult. Repeat Rewrite Rabsolu_Rinv; Try Assumption Orelse DiscrR. Replace (Rabsolu eps) with eps. @@ -174,7 +176,8 @@ Apply Rlt_monotony_r. Apply Rabsolu_pos_lt. Unfold Rdiv; Unfold Rsqr; Repeat Apply prod_neq_R0; Assumption Orelse Idtac. Red; Intro H11; Rewrite H11 in H; Elim (Rlt_antirefl ? H). -Apply Rinv_neq_R0; Repeat Apply prod_neq_R0. +Apply Rinv_neq_R0; Apply prod_neq_R0. +Apply prod_neq_R0. DiscrR. Assumption. Assumption. @@ -193,7 +196,10 @@ Rewrite <- (Rmult_sym ``2``). Unfold Rdiv in H10; Exact H10. Symmetry; Apply Rabsolu_right; Left; Sup0. Right; Unfold Rsqr Rdiv. -Repeat Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. +Rewrite Rinv_Rmult; Try Assumption Orelse DiscrR. Repeat Rewrite Rabsolu_mult. Repeat Rewrite Rabsolu_Rinv; Try Assumption Orelse DiscrR. Replace (Rabsolu eps) with eps. |