diff options
Diffstat (limited to 'theories/Reals/Rtopology.v')
| -rw-r--r-- | theories/Reals/Rtopology.v | 20 |
1 files changed, 11 insertions, 9 deletions
diff --git a/theories/Reals/Rtopology.v b/theories/Reals/Rtopology.v index d21042884e..fa5442e86f 100644 --- a/theories/Reals/Rtopology.v +++ b/theories/Reals/Rtopology.v @@ -12,6 +12,7 @@ Require Import Rbase. Require Import Rfunctions. Require Import Ranalysis1. Require Import RList. +Require Import List. Require Import Classical_Prop. Require Import Classical_Pred_Type. Local Open Scope R_scope. @@ -388,7 +389,7 @@ Record family : Type := mkfamily Definition family_open_set (f:family) : Prop := forall x:R, open_set (f x). Definition domain_finite (D:R -> Prop) : Prop := - exists l : Rlist, (forall x:R, D x <-> In x l). + exists l : list R, (forall x:R, D x <-> In x l). Definition family_finite (f:family) : Prop := domain_finite (ind f). @@ -669,7 +670,7 @@ Proof. intro H14; simpl in H14; unfold intersection_domain in H14; specialize H13 with x0; destruct H13 as (H13,H15); destruct (Req_dec x0 y0) as [H16|H16]. - simpl; left; apply H16. + simpl; left. symmetry; apply H16. simpl; right; apply H13. simpl; unfold intersection_domain; unfold Db in H14; decompose [and or] H14. @@ -678,8 +679,8 @@ Proof. intro H14; simpl in H14; destruct H14 as [H15|H15]; simpl; unfold intersection_domain. split. - apply (cond_fam f0); rewrite H15; exists b; apply H6. - unfold Db; right; assumption. + apply (cond_fam f0); rewrite <- H15; exists b; apply H6. + unfold Db; right; symmetry; assumption. simpl; unfold intersection_domain; elim (H13 x0). intros _ H16; assert (H17 := H16 H15); simpl in H17; unfold intersection_domain in H17; split. @@ -750,15 +751,15 @@ Proof. intro H14; simpl in H14; unfold intersection_domain in H14; specialize (H13 x0); destruct H13 as (H13,H15); destruct (Req_dec x0 y0) as [Heq|Hneq]. - simpl; left; apply Heq. + simpl; left; symmetry; apply Heq. simpl; right; apply H13; simpl; unfold intersection_domain; unfold Db in H14; decompose [and or] H14. split; assumption. elim Hneq; assumption. intros [H15|H15]. split. - apply (cond_fam f0); rewrite H15; exists m; apply H6. - unfold Db; right; assumption. + apply (cond_fam f0); rewrite <- H15; exists m; apply H6. + unfold Db; right; symmetry; assumption. elim (H13 x0); intros _ H16. assert (H17 := H16 H15). simpl in H17. @@ -810,9 +811,10 @@ Proof. unfold family_finite; unfold domain_finite; exists (cons y0 nil); intro; split. simpl; unfold intersection_domain; intros (H3,H4). - unfold D' in H4; left; apply H4. + unfold D' in H4; left; symmetry; apply H4. simpl; unfold intersection_domain; intros [H4|[]]. - split; [ rewrite H4; apply (cond_fam f0); exists a; apply H2 | apply H4 ]. + split; [ rewrite <- H4; apply (cond_fam f0); exists a; apply H2 | + symmetry; apply H4 ]. split; [ right; reflexivity | apply Hle ]. apply compact_eqDom with (fun c:R => False). apply compact_EMP. |