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stdpp
Commits
e767481f
Commit
e767481f
authored
Feb 16, 2016
by
Ralf Jung
Browse files
sts: for disjointness, it is enough to demand being a subset of the empty set
parent
0b7821f1
Changes
1
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Inline
Side-by-side
theories/sets.v
View file @
e767481f
...
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@@ -18,9 +18,9 @@ Instance set_difference {A} : Difference (set A) := λ X1 X2,
Instance
set_collection
:
Collection
A
(
set
A
).
Proof
.
by
split
;
[
split
|
|]
;
repeat
intro
.
Qed
.
Lemma
mkSet_elem_of
{
A
}
(
f
:
A
→
Prop
)
x
:
f
x
→
x
∈
mkSet
f
.
Lemma
mkSet_elem_of
{
A
}
(
f
:
A
→
Prop
)
x
:
(
x
∈
mkSet
f
)
=
f
x
.
Proof
.
done
.
Qed
.
Lemma
mkSet_not_elem_of
{
A
}
(
f
:
A
→
Prop
)
x
:
~f
x
→
x
∉
mkSet
f
.
Lemma
mkSet_not_elem_of
{
A
}
(
f
:
A
→
Prop
)
x
:
(
x
∉
mkSet
f
)
=
(
~f
x
)
.
Proof
.
done
.
Qed
.
Instance
set_ret
:
MRet
set
:
=
λ
A
(
x
:
A
),
{[
x
]}.
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