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Micaela Mayero
Numerical Analysis in Coq
Commits
de7dd977
Commit
de7dd977
authored
2 years ago
by
François Clément
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Renaming (Inter_with_empty -> Inter_wEmpty).
Add results about Inter and Union when adding {empty,full}set.
parent
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Lebesgue/Set_theory/Set_system/Set_system_base_base.v
+31
-2
31 additions, 2 deletions
Lebesgue/Set_theory/Set_system/Set_system_base_base.v
with
31 additions
and
2 deletions
Lebesgue/Set_theory/Set_system/Set_system_base_base.v
+
31
−
2
View file @
de7dd977
...
...
@@ -210,8 +210,8 @@ Proof.
intros
H
A
B
_
HA
HB
;
now
apply
H
.
Qed
.
Lemma
Inter_w
ith_e
mpty
:
Inter
P
->
Inter
(
fun
A
=>
P
A
\
/
A
=
emptyset
).
Lemma
Inter_w
E
mpty
:
Inter
P
->
Inter
(
add
P
emptyset
).
Proof
.
intros
H
A
B
[
HA
|
HA
]
[
HB
|
HB
].
left
;
now
apply
H
.
...
...
@@ -219,6 +219,16 @@ right; rewrite HB; apply inter_emptyset_r.
1
,
2
:
right
;
rewrite
HA
;
apply
inter_emptyset_l
.
Qed
.
Lemma
Inter_wFull
:
Inter
P
->
Inter
(
add
P
fullset
).
Proof
.
intros
H
A
B
[
HA
|
HA
]
[
HB
|
HB
].
left
;
now
apply
H
.
left
;
now
rewrite
HB
,
inter_fullset_r
.
left
;
now
rewrite
HA
,
inter_fullset_l
.
right
;
now
rewrite
HA
,
HB
,
inter_fullset_l
.
Qed
.
Lemma
Inter_Diff
:
Compl
P
->
Inter
P
->
Diff
P
.
Proof
.
...
...
@@ -263,6 +273,25 @@ now apply Inter_Diff.
apply
Diff_Inter
.
Qed
.
Lemma
Union_wEmpty
:
Union
P
->
Union
(
add
P
emptyset
).
Proof
.
intros
H
A
B
[
HA
|
HA
]
[
HB
|
HB
].
left
;
now
apply
H
.
left
;
now
rewrite
HB
,
union_emptyset_r
.
left
;
now
rewrite
HA
,
union_emptyset_l
.
right
;
now
rewrite
HA
,
HB
,
union_emptyset_l
.
Qed
.
Lemma
Union_wFull
:
Union
P
->
Union
(
add
P
fullset
).
Proof
.
intros
H
A
B
[
HA
|
HA
]
[
HB
|
HB
].
left
;
now
apply
H
.
right
;
rewrite
HB
;
apply
union_fullset_r
.
1
,
2
:
right
;
rewrite
HA
;
apply
union_fullset_l
.
Qed
.
Lemma
Union_disj_Union
:
Diff
P
->
Union_disj
P
->
Union
P
.
Proof
.
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