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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Let x2 of type
ι
be given.
Assume H0:
x2
∈
x0
.
Apply binunionI1 with
{
Inj0
x3
|x3 ∈
x0
}
,
{
Inj1
x3
|x3 ∈
x1
}
,
Inj0
x2
.
Apply ReplI with
x0
,
Inj0
,
x2
.
The subproof is completed by applying H0.
■