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Proofgold Proof
pf
Claim L0:
...
...
Apply unknownprop_98dce570015dab8b9107dc33a5e2e4ea0417c490e1cfe00b91b6267d26e82089 with
λ x0 x1 .
(
λ x2 x3 .
and
(
and
(
and
(
and
(
and
(
80242..
(
bc82c..
x2
x3
)
)
(
∀ x4 .
prim1
x4
(
23e07..
x2
)
⟶
099f3..
(
bc82c..
x4
x3
)
(
bc82c..
x2
x3
)
)
)
(
∀ x4 .
prim1
x4
(
5246e..
x2
)
⟶
099f3..
(
bc82c..
x2
x3
)
(
bc82c..
x4
x3
)
)
)
(
∀ x4 .
prim1
x4
(
23e07..
x3
)
⟶
099f3..
(
bc82c..
x2
x4
)
(
bc82c..
x2
x3
)
)
)
(
∀ x4 .
prim1
x4
(
5246e..
x3
)
⟶
099f3..
(
bc82c..
x2
x3
)
(
bc82c..
x2
x4
)
)
)
(
02b90..
(
0ac37..
(
94f9e..
(
23e07..
x2
)
(
λ x4 .
bc82c..
x4
x3
)
)
(
94f9e..
(
23e07..
x3
)
(
λ x4 .
bc82c..
x2
x4
)
)
)
(
0ac37..
(
94f9e..
(
5246e..
x2
)
(
λ x4 .
bc82c..
x4
x3
)
)
(
94f9e..
(
5246e..
x3
)
(
λ x4 .
bc82c..
x2
x4
)
)
)
)
)
x0
x1
.
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Assume H1:
80242..
x0
.
Assume H2:
80242..
x1
.
Assume H3:
∀ x2 .
prim1
x2
(
56ded..
(
e4431..
x0
)
)
⟶
(
λ x3 x4 .
and
(
and
(
and
(
and
(
and
(
80242..
(
bc82c..
x3
x4
)
)
(
∀ x5 .
prim1
x5
(
23e07..
x3
)
⟶
099f3..
(
bc82c..
x5
x4
)
(
bc82c..
x3
x4
)
)
)
(
∀ x5 .
prim1
x5
(
5246e..
x3
)
⟶
099f3..
(
bc82c..
x3
x4
)
(
bc82c..
x5
x4
)
)
)
(
∀ x5 .
prim1
x5
(
23e07..
x4
)
⟶
099f3..
(
bc82c..
x3
x5
)
(
bc82c..
x3
x4
)
)
)
(
∀ x5 .
prim1
x5
(
5246e..
x4
)
⟶
099f3..
(
bc82c..
x3
x4
)
(
bc82c..
x3
x5
)
)
)
(
02b90..
(
0ac37..
(
94f9e..
(
23e07..
x3
)
(
λ x5 .
bc82c..
x5
x4
)
)
(
94f9e..
(
23e07..
x4
)
(
λ x5 .
bc82c..
x3
x5
)
)
)
(
0ac37..
(
94f9e..
(
5246e..
x3
)
(
λ x5 .
bc82c..
x5
x4
)
)
(
94f9e..
(
5246e..
x4
)
(
λ x5 .
bc82c..
x3
x5
)
)
)
)
)
x2
x1
.
Assume H4:
∀ x2 .
...
⟶
(
λ x3 x4 .
and
(
and
(
and
(
and
(
and
(
80242..
(
bc82c..
x3
x4
)
)
(
∀ x5 .
prim1
x5
(
23e07..
x3
)
⟶
099f3..
(
bc82c..
x5
x4
)
(
bc82c..
x3
x4
)
)
)
(
∀ x5 .
prim1
x5
(
5246e..
x3
)
⟶
099f3..
(
bc82c..
x3
x4
)
(
bc82c..
x5
x4
)
)
)
(
∀ x5 .
prim1
x5
(
23e07..
x4
)
⟶
099f3..
(
bc82c..
x3
x5
)
(
bc82c..
x3
x4
)
)
)
(
∀ x5 .
prim1
...
...
⟶
099f3..
(
bc82c..
x3
x4
)
(
bc82c..
x3
x5
)
)
)
...
)
...
...
.
...
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