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| 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/SeqProp.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/SeqProp.v')
| -rw-r--r-- | theories/Reals/SeqProp.v | 12 |
1 files changed, 5 insertions, 7 deletions
diff --git a/theories/Reals/SeqProp.v b/theories/Reals/SeqProp.v index 7f3282a35..d8f1cc6aa 100644 --- a/theories/Reals/SeqProp.v +++ b/theories/Reals/SeqProp.v @@ -461,8 +461,7 @@ Lemma cond_eq : forall x y:R, (forall eps:R, 0 < eps -> Rabs (x - y) < eps) -> x = y. Proof. intros. - case (total_order_T x y); intro. - elim s; intro. + destruct (total_order_T x y) as [[Hlt|Heq]|Hgt]. cut (0 < y - x). intro. assert (H1 := H (y - x) H0). @@ -897,8 +896,7 @@ Lemma growing_ineq : forall (Un:nat -> R) (l:R), Un_growing Un -> Un_cv Un l -> forall n:nat, Un n <= l. Proof. - intros; case (total_order_T (Un n) l); intro. - elim s; intro. + intros; destruct (total_order_T (Un n) l) as [[Hlt|Heq]|Hgt]. left; assumption. right; assumption. cut (0 < Un n - l). @@ -1103,11 +1101,11 @@ Proof. apply (cv_infty_cv_R0 (fun n:nat => INR (S n))). intro; apply not_O_INR; discriminate. assumption. - unfold cv_infty; intro; case (total_order_T M0 0); intro. - elim s; intro. + unfold cv_infty; intro; + destruct (total_order_T M0 0) as [[Hlt|Heq]|Hgt]. exists 0%nat; intros. apply Rlt_trans with 0; [ assumption | apply lt_INR_0; apply lt_O_Sn ]. - exists 0%nat; intros; rewrite b; apply lt_INR_0; apply lt_O_Sn. + exists 0%nat; intros; rewrite Heq; apply lt_INR_0; apply lt_O_Sn. set (M0_z := up M0). assert (H10 := archimed M0). cut (0 <= M0_z)%Z. |