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Proofgold Asset
asset id
21ee9296df36b705ca8b3b77229d07c775f15df3ad007bd070a9b8534583c1b1
asset hash
275c4d0256e44868b1a2e816672132f68783f387590409d4e5d877a7272c94b5
bday / block
18593
tx
f78d3..
preasset
doc published by
Pr4zB..
Param
ChurchNum_3ary_proj_p
:
(
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
CN (
ι
→
ι
)
) →
ο
Param
ChurchNum_8ary_proj_p
:
(
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
CN (
ι
→
ι
)
) →
ο
Definition
TwoRamseyGraph_4_5_24_ChurchNums_3x8
:=
λ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x2 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x4 .
x0
(
x1
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
)
)
(
x1
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
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x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
)
(
x2
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
x5
)
)
)
)
(
λ x5 .
x4
)
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Param
ChurchNums_3x8_eq
:
(
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
CN (
ι
→
ι
)
) →
(
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
CN (
ι
→
ι
)
) →
(
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
CN (
ι
→
ι
)
) →
(
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
(
(
ι
→
ι
) →
ι
→
ι
) →
CN (
ι
→
ι
)
) →
ο
Definition
ChurchNums_3x8_neq
:=
λ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x2 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
not
(
ChurchNums_3x8_eq
x0
x1
x2
x3
)
Known
fc1b4..
:
∀ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_8ary_proj_p
x1
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x3 x4 x5 :
(
ι → ι
)
→
ι → ι
.
x3
)
(
λ x3 x4 x5 x6 x7 x8 x9 x10 :
(
ι → ι
)
→
ι → ι
.
x3
)
x0
x1
=
λ x3 x4 .
x3
)
⟶
∀ x2 : ο .
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x11
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x10
)
⟶
x2
)
⟶
(
(
x0
=
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
(
x1
=
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x11
)
⟶
x2
)
⟶
x2
Known
f6916..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x0
=
x1
⟶
x2
=
x3
⟶
ChurchNums_3x8_eq
x0
x2
x1
x3
Known
fa458..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_8ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x0
x2
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x1
x3
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x6
)
x0
x2
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x6
)
x1
x3
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x2
x1
x3
=
λ x5 x6 .
x5
)
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x0
x2
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x5
)
x0
x2
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x1
x3
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x5
)
x1
x3
⟶
ChurchNums_3x8_neq
x0
x2
x1
x3
⟶
False
Known
639c7..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_8ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x0
x2
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x1
x3
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x7
)
x0
x2
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x7
)
x1
x3
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x2
x1
x3
=
λ x5 x6 .
x5
)
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x0
x2
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x6
)
x0
x2
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x1
x3
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x6
)
x1
x3
⟶
ChurchNums_3x8_neq
x0
x2
x1
x3
⟶
False
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Known
99ba2..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_8ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x0
x2
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x1
x3
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x0
x2
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x5
)
x1
x3
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x2
x1
x3
=
λ x5 x6 .
x5
)
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x0
x2
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x0
x2
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x1
x3
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x4
)
x1
x3
⟶
ChurchNums_3x8_neq
x0
x2
x1
x3
⟶
False
Definition
ChurchNums_8_perm_0_7_6_5_4_3_2_1
:=
λ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x1 x2 x3 x4 x5 x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x0
x1
x8
x7
x6
x5
x4
x3
x2
Definition
ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2
:=
λ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
λ x2 x3 x4 :
(
ι → ι
)
→
ι → ι
.
x0
(
x1
x2
x4
x4
x4
x4
x4
x4
x4
)
(
x1
x4
x3
x3
x3
x3
x3
x3
x3
)
(
x1
x3
x2
x2
x2
x2
x2
x2
x2
)
Known
424ab..
:
∀ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_8ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2
x0
x1
)
Known
6bdd9..
:
∀ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_8ary_proj_p
(
ChurchNums_8_perm_0_7_6_5_4_3_2_1
x0
)
Known
33bbb..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_8ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x2
x1
x3
=
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2
x0
x2
)
(
ChurchNums_8_perm_0_7_6_5_4_3_2_1
x2
)
(
ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2
x1
x3
)
(
ChurchNums_8_perm_0_7_6_5_4_3_2_1
x3
)
Known
cef55..
:
ChurchNum_3ary_proj_p
(
λ x0 x1 x2 :
(
ι → ι
)
→
ι → ι
.
x0
)
Known
208f3..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x0
)
Known
a5963..
:
ChurchNum_3ary_proj_p
(
λ x0 x1 x2 :
(
ι → ι
)
→
ι → ι
.
x2
)
Known
080b7..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
ChurchNums_3x8_eq
(
ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2
x0
x2
)
(
ChurchNums_8_perm_0_7_6_5_4_3_2_1
x2
)
(
ChurchNums_3x8_3_lt1_swap_1_2_ge1_rot2
x1
x3
)
(
ChurchNums_8_perm_0_7_6_5_4_3_2_1
x3
)
⟶
ChurchNums_3x8_eq
x0
x2
x1
x3
Known
94187..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x6
)
Known
7734d..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x7
)
Theorem
59f06..
:
∀ x0 x1 x2 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x3 x4 x5 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
ChurchNum_8ary_proj_p
x4
⟶
ChurchNum_8ary_proj_p
x5
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x7 x8 x9 x10 x11 x12 x13 x14 :
(
ι → ι
)
→
ι → ι
.
x7
)
x0
x3
=
λ x7 x8 .
x7
)
⟶
not
(
∀ x6 : ο .
(
(
x0
=
λ x8 x9 x10 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
(
x3
=
λ x8 x9 x10 x11 x12 x13 x14 x15 :
(
ι → ι
)
→
ι → ι
.
x12
)
⟶
x6
)
⟶
(
(
x0
=
λ x8 x9 x10 :
(
ι → ι
)
→
ι → ι
.
x9
)
⟶
(
x3
=
λ x8 x9 x10 x11 x12 x13 x14 x15 :
(
ι → ι
)
→
ι → ι
.
x9
)
⟶
x6
)
⟶
(
(
x0
=
λ x8 x9 x10 :
(
ι → ι
)
→
ι → ι
.
x9
)
⟶
(
x3
=
λ x8 x9 x10 x11 x12 x13 x14 x15 :
(
ι → ι
)
→
ι → ι
.
x15
)
⟶
x6
)
⟶
(
(
x0
=
λ x8 x9 x10 :
(
ι → ι
)
→
ι → ι
.
x10
)
⟶
(
x3
=
λ x8 x9 x10 x11 x12 x13 x14 x15 :
(
ι → ι
)
→
ι → ι
.
x12
)
⟶
x6
)
⟶
x6
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x7 x8 x9 x10 x11 x12 x13 x14 :
(
ι → ι
)
→
ι → ι
.
x7
)
x1
x4
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x7 x8 x9 x10 x11 x12 x13 x14 :
(
ι → ι
)
→
ι → ι
.
x7
)
x2
x5
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x3
x1
x4
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x3
x2
x5
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x1
x4
x2
x5
=
λ x7 x8 .
x7
)
⟶
ChurchNums_3x8_neq
(
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x6
)
x0
x3
⟶
ChurchNums_3x8_neq
(
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x6
)
x1
x4
⟶
ChurchNums_3x8_neq
(
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x6
)
x2
x5
⟶
ChurchNums_3x8_neq
x0
x3
x1
x4
⟶
ChurchNums_3x8_neq
x0
x3
x2
x5
⟶
ChurchNums_3x8_neq
x1
x4
x2
x5
⟶
False
(proof)
Definition
or
or
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x2
)
⟶
(
x1
⟶
x2
)
⟶
x2
Known
xm
xm
:
∀ x0 : ο .
or
x0
(
not
x0
)
Known
a5d1b..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
(
∀ x4 : ο .
(
(
x0
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
(
x2
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x10
)
⟶
x4
)
⟶
(
(
x0
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x7
)
⟶
(
x2
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x7
)
⟶
x4
)
⟶
(
(
x0
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x7
)
⟶
(
x2
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x13
)
⟶
x4
)
⟶
(
(
x0
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
(
x2
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x10
)
⟶
x4
)
⟶
x4
)
⟶
(
∀ x4 : ο .
(
(
x1
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
(
x3
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x10
)
⟶
x4
)
⟶
(
(
x1
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x7
)
⟶
(
x3
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x7
)
⟶
x4
)
⟶
(
(
x1
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x7
)
⟶
(
x3
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x13
)
⟶
x4
)
⟶
(
(
x1
=
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
(
x3
=
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x10
)
⟶
x4
)
⟶
x4
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x9
)
x0
x2
=
λ x5 x6 .
x5
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
(
λ x5 x6 x7 x8 x9 x10 x11 x12 :
(
ι → ι
)
→
ι → ι
.
x9
)
x1
x3
=
λ x5 x6 .
x5
)
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x8
)
x0
x2
⟶
ChurchNums_3x8_neq
(
λ x4 x5 x6 :
(
ι → ι
)
→
ι → ι
.
x4
)
(
λ x4 x5 x6 x7 x8 x9 x10 x11 :
(
ι → ι
)
→
ι → ι
.
x8
)
x1
x3
⟶
ChurchNums_3x8_neq
x0
x2
x1
x3
⟶
False
Known
bfc1e..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_3x8_neq
x0
x2
x1
x3
⟶
ChurchNums_3x8_neq
x1
x3
x0
x2
Known
f60cd..
:
∀ x0 x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_8ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x2
x1
x3
=
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x1
x3
x0
x2
Known
3a83b..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x4
)
Known
768c1..
:
(
(
λ x1 x2 .
x2
)
=
λ x1 x2 .
x1
)
⟶
∀ x0 : ο .
x0
Theorem
9fe18..
:
∀ x0 x1 x2 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x3 x4 x5 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
ChurchNum_8ary_proj_p
x4
⟶
ChurchNum_8ary_proj_p
x5
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x7 x8 x9 x10 x11 x12 x13 x14 :
(
ι → ι
)
→
ι → ι
.
x7
)
x0
x3
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x7 x8 x9 x10 x11 x12 x13 x14 :
(
ι → ι
)
→
ι → ι
.
x7
)
x1
x4
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
λ x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x7
)
(
λ x7 x8 x9 x10 x11 x12 x13 x14 :
(
ι → ι
)
→
ι → ι
.
x7
)
x2
x5
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x3
x1
x4
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x3
x2
x5
=
λ x7 x8 .
x7
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x1
x4
x2
x5
=
λ x7 x8 .
x7
)
⟶
ChurchNums_3x8_neq
(
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x6
)
x0
x3
⟶
ChurchNums_3x8_neq
(
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x6
)
x1
x4
⟶
ChurchNums_3x8_neq
(
λ x6 x7 x8 :
(
ι → ι
)
→
ι → ι
.
x6
)
(
λ x6 x7 x8 x9 x10 x11 x12 x13 :
(
ι → ι
)
→
ι → ι
.
x6
)
x2
x5
⟶
ChurchNums_3x8_neq
x0
x3
x1
x4
⟶
ChurchNums_3x8_neq
x0
x3
x2
x5
⟶
ChurchNums_3x8_neq
x1
x4
x2
x5
⟶
False
(proof)