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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Apply unknownprop_5211365bd8f9bc32132c7d18ef8b1eeb82945bf78b11eab7df690b661bcac67c with
x0
,
x1
,
0
,
λ x2 x3 .
x3
=
ad280..
x0
x1
.
Apply Repl_Empty with
λ x2 .
SetAdjoin
x2
(
Sing
3
)
,
λ x2 x3 .
binunion
(
binunion
x0
{
(
λ x5 .
SetAdjoin
x5
(
Sing
2
)
)
x4
|x4 ∈
x1
}
)
x3
=
ad280..
x0
x1
.
Apply binunion_idr with
binunion
x0
{
(
λ x3 .
SetAdjoin
x3
(
Sing
2
)
)
x2
|x2 ∈
x1
}
,
λ x2 x3 .
x3
=
ad280..
x0
x1
.
Let x2 of type
ι
→
ι
→
ο
be given.
Assume H0:
x2
(
binunion
x0
{
(
λ x4 .
SetAdjoin
x4
(
Sing
2
)
)
x3
|x3 ∈
x1
}
)
(
ad280..
x0
x1
)
.
The subproof is completed by applying H0.
■