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stdpp
Commits
9bfa00b2
Commit
9bfa00b2
authored
Jun 18, 2018
by
Ralf Jung
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add lemma about chained difference
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e1e5349a
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theories/collections.v
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theories/collections.v
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9bfa00b2
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@@ -622,7 +622,8 @@ Section collection.
Proof
.
set_solver
.
Qed
.
Lemma
subset_difference_elem_of
{
x
:
A
}
{
s
:
C
}
(
inx
:
x
∈
s
)
:
s
∖
{[
x
]}
⊂
s
.
Proof
.
set_solver
.
Qed
.
Lemma
difference_difference
X
Y
Z
:
(
X
∖
Y
)
∖
Z
≡
X
∖
(
Y
∪
Z
).
Proof
.
set_solver
.
Qed
.
Lemma
difference_mono
X1
X2
Y1
Y2
:
X1
⊆
X2
→
Y2
⊆
Y1
→
X1
∖
Y1
⊆
X2
∖
Y2
.
...
...
@@ -688,6 +689,8 @@ Section collection.
Proof
.
unfold_leibniz
.
apply
difference_intersection_distr_l
.
Qed
.
Lemma
difference_disjoint_L
X
Y
:
X
##
Y
→
X
∖
Y
=
X
.
Proof
.
unfold_leibniz
.
apply
difference_disjoint
.
Qed
.
Lemma
difference_difference_L
X
Y
Z
:
(
X
∖
Y
)
∖
Z
=
X
∖
(
Y
∪
Z
).
Proof
.
unfold_leibniz
.
apply
difference_difference
.
Qed
.
(** Disjointness *)
Lemma
disjoint_intersection_L
X
Y
:
X
##
Y
↔
X
∩
Y
=
∅
.
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