dan
/
HITs-Examples
mirror of https://github.com/nmvdw/HITs-Examples
1
0
Fork 0
Code Issues Releases Wiki Activity

Some cleaning

This commit is contained in:
Niels van der Weide 2017-09-21 18:13:34 +02:00
parent f4253520c8
commit 7b5bc340ff
1 changed files with 4 additions and 10 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

14
FiniteSets/kuratowski/length.v
View File

@ -81,13 +81,9 @@ Section Length.
simple refine (FSet_cons_ind (fun Z => _) _ _ _ _ _ X) simple refine (FSet_cons_ind (fun Z => _) _ _ _ _ _ X)
; try (intros ; apply path_ishprop) ; simpl. ; try (intros ; apply path_ishprop) ; simpl.
- intros. - intros.
rewrite nl. apply (ap length (nl _)).
reflexivity.
- intros a X1 HX1 HX1Y. - intros a X1 HX1 HX1Y.
rewrite <- assoc. rewrite <- assoc, ?length_compute, ?union_isIn_d in *.
rewrite ?length_compute.
rewrite ?union_isIn_d in *.
unfold disjoint in HX1Y.
pose (ap (fun Z => a ∈_d Z) HX1Y) as p. pose (ap (fun Z => a ∈_d Z) HX1Y) as p.
simpl in p. simpl in p.
rewrite intersection_isIn_d, union_isIn_d, singleton_isIn_d_aa, empty_isIn_d in p. rewrite intersection_isIn_d, union_isIn_d, singleton_isIn_d_aa, empty_isIn_d in p.
@ -96,10 +92,8 @@ Section Length.
contradiction true_ne_false. contradiction true_ne_false.
} }
rewrite ?HaY, HX1. rewrite ?HaY, HX1.
destruct (a ∈_d X1). destruct (a ∈_d X1) ; try reflexivity.
* reflexivity. apply (disjoint_sub a X1 Y HX1Y).
* reflexivity.
* apply (disjoint_sub a X1 Y HX1Y).
Defined. Defined.
Lemma set_as_difference X Y : X = (difference X Y) ∪ (X ∩ Y). Lemma set_as_difference X Y : X = (difference X Y) ∪ (X ∩ Y).