diff options
| author |  Hugo Herbelin <Hugo.Herbelin@inria.fr> | 2014-06-01 10:26:26 +0200 |
|---|---|---|
| committer | Hugo Herbelin <Hugo.Herbelin@inria.fr> | 2014-06-01 11:33:55 +0200 |
| commit | 76adb57c72fccb4f3e416bd7f3927f4fff72178b (patch) | |
| tree | f8d72073a2ea62d3e5c274c201ef06532ac57b61 /theories/Reals/Ranalysis4.v | |
| parent | be01deca2b8ff22505adaa66f55f005673bf2d85 (diff) | |
Making those proofs which depend on names generated for the arguments
in Prop of constructors of inductive types independent of these names.
Incidentally upgraded/simplified a couple of proofs, mainly in Reals.
This prepares to the next commit about using names based on H for such
hypotheses in Prop.
Diffstat (limited to 'theories/Reals/Ranalysis4.v')
| -rw-r--r-- | theories/Reals/Ranalysis4.v | 21 |
1 files changed, 10 insertions, 11 deletions
diff --git a/theories/Reals/Ranalysis4.v b/theories/Reals/Ranalysis4.v index 45c79af48..663f62f7a 100644 --- a/theories/Reals/Ranalysis4.v +++ b/theories/Reals/Ranalysis4.v @@ -117,14 +117,14 @@ Proof. rewrite Rplus_opp_r; rewrite Rabs_R0; apply H0. apply H1. apply Rle_ge. - case (Rcase_abs h); intro. - rewrite (Rabs_left h r) in H2. + destruct (Rcase_abs h) as [Hlt|Hgt]. + rewrite (Rabs_left h Hlt) in H2. left; rewrite Rplus_comm; apply Rplus_lt_reg_l with (- h); rewrite Rplus_0_r; rewrite <- Rplus_assoc; rewrite Rplus_opp_l; rewrite Rplus_0_l; apply H2. apply Rplus_le_le_0_compat. left; apply H. - apply Rge_le; apply r. + apply Rge_le; apply Hgt. left; apply H. Qed. @@ -145,12 +145,12 @@ Proof. rewrite <- Rinv_r_sym. rewrite Ropp_involutive; rewrite Rplus_opp_l; rewrite Rabs_R0; apply H0. apply H2. - case (Rcase_abs h); intro. + destruct (Rcase_abs h) as [Hlt|Hgt]. apply Ropp_lt_cancel. rewrite Ropp_0; rewrite Ropp_plus_distr; apply Rplus_lt_0_compat. apply H1. - apply Ropp_0_gt_lt_contravar; apply r. - rewrite (Rabs_right h r) in H3. + apply Ropp_0_gt_lt_contravar; apply Hlt. + rewrite (Rabs_right h Hgt) in H3. apply Rplus_lt_reg_l with (- x); rewrite Rplus_0_r; rewrite <- Rplus_assoc; rewrite Rplus_opp_l; rewrite Rplus_0_l; apply H3. apply H. @@ -161,13 +161,12 @@ Qed. Lemma Rderivable_pt_abs : forall x:R, x <> 0 -> derivable_pt Rabs x. Proof. intros. - case (total_order_T x 0); intro. - elim s; intro. + destruct (total_order_T x 0) as [[Hlt|Heq]|Hgt]. unfold derivable_pt; exists (-1). - apply (Rabs_derive_2 x a). - elim H; exact b. + apply (Rabs_derive_2 x Hlt). + elim H; exact Heq. unfold derivable_pt; exists 1. - apply (Rabs_derive_1 x r). + apply (Rabs_derive_1 x Hgt). Qed. (** Rabsolu is continuous for all x *) |