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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
→
ι
be given.
Let x2 of type
ι
be given.
Assume H0:
prim1
x2
(
0fc90..
x0
(
λ x3 .
x1
x3
)
)
.
Apply and3E with
aae7a..
(
e76d4..
x2
)
(
22ca9..
x2
)
=
x2
,
prim1
(
e76d4..
x2
)
x0
,
prim1
(
22ca9..
x2
)
(
x1
(
e76d4..
x2
)
)
,
aae7a..
(
e76d4..
x2
)
(
22ca9..
x2
)
=
x2
leaving 2 subgoals.
Apply unknownprop_4861fab3b9bde4ccc5c91f323e4d2535c7d435027e9067e34ce3781cfa602d01 with
x0
,
x1
,
x2
.
The subproof is completed by applying H0.
Assume H1:
aae7a..
(
e76d4..
x2
)
(
22ca9..
x2
)
=
x2
.
Assume H2:
prim1
(
e76d4..
x2
)
x0
.
Assume H3:
prim1
(
22ca9..
x2
)
(
x1
(
e76d4..
x2
)
)
.
The subproof is completed by applying H1.
■