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Proofgold Asset
asset id
07554dc55baba3d5409c36cbee37b2a706b66e068a97f8a7632a6114602cf3ef
asset hash
3536145730525832174a803f6f5ba33f14964f315dac910f926c4c15ced135c8
bday / block
18661
tx
e4dd4..
preasset
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Pr4zB..
Definition
ChurchNum_8ary_proj_p
:=
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
.
∀ 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
)
→ ο
.
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x2
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x3
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x6
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x7
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 :
(
ι → ι
)
→
ι → ι
.
x9
)
⟶
x1
x0
Param
ChurchNum_3ary_proj_p
:
(
(
(
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
.
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)
(
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
)
)
)
(
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
.
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
)
)
(
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
)
)
)
(
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
ChurchNums_8_perm_1_2_3_4_5_6_7_0
:=
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
x2
x3
x4
x5
x6
x7
x8
x1
Definition
ChurchNums_8_perm_7_0_1_2_3_4_5_6
:=
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
x8
x1
x2
x3
x4
x5
x6
x7
Param
ChurchNums_8x3_lt1_id_ge1_rot1
:
(
(
(
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
) →
CN (
ι
→
ι
)
Param
ChurchNums_8x3_lt1_id_ge1_rot2
:
(
(
(
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
) →
CN (
ι
→
ι
)
Known
b0f0d..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt1_id_ge1_rot2
x0
x1
)
Known
0bfaf..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt1_id_ge1_rot1
x0
x1
)
Known
c2824..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt1_id_ge1_rot2
x0
(
ChurchNums_8x3_lt1_id_ge1_rot1
x0
x1
)
=
x1
Known
b782a..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt1_id_ge1_rot1
x0
(
ChurchNums_8x3_lt1_id_ge1_rot2
x0
x1
)
=
x1
Known
e1672..
:
∀ 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_7_0_1_2_3_4_5_6
x0
)
Known
4ac5f..
:
∀ 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_1_2_3_4_5_6_7_0
x0
)
Known
06461..
:
∀ 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
.
ChurchNums_8_perm_7_0_1_2_3_4_5_6
(
ChurchNums_8_perm_1_2_3_4_5_6_7_0
x0
)
=
x0
Known
accc4..
:
∀ 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
.
ChurchNums_8_perm_1_2_3_4_5_6_7_0
(
ChurchNums_8_perm_7_0_1_2_3_4_5_6
x0
)
=
x0
Known
71c84..
:
∀ 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_8x3_lt1_id_ge1_rot2
x2
x0
)
(
ChurchNums_8_perm_7_0_1_2_3_4_5_6
x2
)
(
ChurchNums_8x3_lt1_id_ge1_rot2
x3
x1
)
(
ChurchNums_8_perm_7_0_1_2_3_4_5_6
x3
)
Definition
ChurchNums_8_perm_2_3_4_5_6_7_0_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
x3
x4
x5
x6
x7
x8
x1
x2
Definition
ChurchNums_8_perm_6_7_0_1_2_3_4_5
:=
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
x7
x8
x1
x2
x3
x4
x5
x6
Param
ChurchNums_8x3_lt2_id_ge2_rot1
:
(
(
(
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
) →
CN (
ι
→
ι
)
Param
ChurchNums_8x3_lt2_id_ge2_rot2
:
(
(
(
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
) →
CN (
ι
→
ι
)
Known
16e4b..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt2_id_ge2_rot2
x0
x1
)
Known
1d5ae..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt2_id_ge2_rot1
x0
x1
)
Known
0e9d3..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt2_id_ge2_rot2
x0
(
ChurchNums_8x3_lt2_id_ge2_rot1
x0
x1
)
=
x1
Known
53c9b..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt2_id_ge2_rot1
x0
(
ChurchNums_8x3_lt2_id_ge2_rot2
x0
x1
)
=
x1
Known
a5ec6..
:
∀ 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_6_7_0_1_2_3_4_5
x0
)
Known
c5de4..
:
∀ 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_2_3_4_5_6_7_0_1
x0
)
Known
abce4..
:
∀ 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
.
ChurchNums_8_perm_6_7_0_1_2_3_4_5
(
ChurchNums_8_perm_2_3_4_5_6_7_0_1
x0
)
=
x0
Known
13c67..
:
∀ 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
.
ChurchNums_8_perm_2_3_4_5_6_7_0_1
(
ChurchNums_8_perm_6_7_0_1_2_3_4_5
x0
)
=
x0
Known
a486a..
:
∀ 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_8x3_lt2_id_ge2_rot2
x2
x0
)
(
ChurchNums_8_perm_6_7_0_1_2_3_4_5
x2
)
(
ChurchNums_8x3_lt2_id_ge2_rot2
x3
x1
)
(
ChurchNums_8_perm_6_7_0_1_2_3_4_5
x3
)
Definition
ChurchNums_8_perm_3_4_5_6_7_0_1_2
:=
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
x4
x5
x6
x7
x8
x1
x2
x3
Definition
ChurchNums_8_perm_5_6_7_0_1_2_3_4
:=
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
x6
x7
x8
x1
x2
x3
x4
x5
Param
ChurchNums_8x3_lt3_id_ge3_rot1
:
(
(
(
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
) →
CN (
ι
→
ι
)
Param
ChurchNums_8x3_to_3_lt3_id_ge3_rot2
:
(
(
(
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
) →
CN (
ι
→
ι
)
Known
ec90a..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_to_3_lt3_id_ge3_rot2
x0
x1
)
Known
f7f04..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt3_id_ge3_rot1
x0
x1
)
Known
92519..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_to_3_lt3_id_ge3_rot2
x0
(
ChurchNums_8x3_lt3_id_ge3_rot1
x0
x1
)
=
x1
Known
28253..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt3_id_ge3_rot1
x0
(
ChurchNums_8x3_to_3_lt3_id_ge3_rot2
x0
x1
)
=
x1
Known
eed30..
:
∀ 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_5_6_7_0_1_2_3_4
x0
)
Known
eaaf4..
:
∀ 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_3_4_5_6_7_0_1_2
x0
)
Known
44285..
:
∀ 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
.
ChurchNums_8_perm_5_6_7_0_1_2_3_4
(
ChurchNums_8_perm_3_4_5_6_7_0_1_2
x0
)
=
x0
Known
d720a..
:
∀ 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
.
ChurchNums_8_perm_3_4_5_6_7_0_1_2
(
ChurchNums_8_perm_5_6_7_0_1_2_3_4
x0
)
=
x0
Known
693c5..
:
∀ 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_8x3_to_3_lt3_id_ge3_rot2
x2
x0
)
(
ChurchNums_8_perm_5_6_7_0_1_2_3_4
x2
)
(
ChurchNums_8x3_to_3_lt3_id_ge3_rot2
x3
x1
)
(
ChurchNums_8_perm_5_6_7_0_1_2_3_4
x3
)
Definition
ChurchNums_8_perm_4_5_6_7_0_1_2_3
:=
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
x5
x6
x7
x8
x1
x2
x3
x4
Param
ChurchNums_8x3_lt4_id_ge4_rot1
:
(
(
(
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
) →
CN (
ι
→
ι
)
Param
ChurchNums_8x3_to_3_lt4_id_ge4_rot2
:
(
(
(
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
) →
CN (
ι
→
ι
)
Known
24233..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_to_3_lt4_id_ge4_rot2
x0
x1
)
Known
b68fb..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt4_id_ge4_rot1
x0
x1
)
Known
ad374..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_to_3_lt4_id_ge4_rot2
x0
(
ChurchNums_8x3_lt4_id_ge4_rot1
x0
x1
)
=
x1
Known
49e33..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt4_id_ge4_rot1
x0
(
ChurchNums_8x3_to_3_lt4_id_ge4_rot2
x0
x1
)
=
x1
Known
dac10..
:
∀ 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_4_5_6_7_0_1_2_3
x0
)
Known
5a925..
:
∀ 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
.
ChurchNums_8_perm_4_5_6_7_0_1_2_3
(
ChurchNums_8_perm_4_5_6_7_0_1_2_3
x0
)
=
x0
Known
1bd40..
:
∀ 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_8x3_to_3_lt4_id_ge4_rot2
x2
x0
)
(
ChurchNums_8_perm_4_5_6_7_0_1_2_3
x2
)
(
ChurchNums_8x3_to_3_lt4_id_ge4_rot2
x3
x1
)
(
ChurchNums_8_perm_4_5_6_7_0_1_2_3
x3
)
Param
ChurchNums_8x3_lt5_id_ge5_rot1
:
(
(
(
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
) →
CN (
ι
→
ι
)
Param
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
:
(
(
(
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
) →
CN (
ι
→
ι
)
Known
7b754..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
x0
x1
)
Known
a776d..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt5_id_ge5_rot1
x0
x1
)
Known
a48ad..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
x0
(
ChurchNums_8x3_lt5_id_ge5_rot1
x0
x1
)
=
x1
Known
b1cc9..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt5_id_ge5_rot1
x0
(
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
x0
x1
)
=
x1
Known
84d56..
:
∀ 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_8x3_to_3_lt5_id_ge5_rot2
x2
x0
)
(
ChurchNums_8_perm_3_4_5_6_7_0_1_2
x2
)
(
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
x3
x1
)
(
ChurchNums_8_perm_3_4_5_6_7_0_1_2
x3
)
Param
ChurchNums_8x3_lt6_id_ge6_rot1
:
(
(
(
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
) →
CN (
ι
→
ι
)
Param
ChurchNums_8x3_to_3_lt6_id_ge6_rot2
:
(
(
(
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
) →
CN (
ι
→
ι
)
Known
2f553..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_to_3_lt6_id_ge6_rot2
x0
x1
)
Known
6c736..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt6_id_ge6_rot1
x0
x1
)
Known
fa851..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_to_3_lt6_id_ge6_rot2
x0
(
ChurchNums_8x3_lt6_id_ge6_rot1
x0
x1
)
=
x1
Known
8922d..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt6_id_ge6_rot1
x0
(
ChurchNums_8x3_to_3_lt6_id_ge6_rot2
x0
x1
)
=
x1
Known
1928f..
:
∀ 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_8x3_to_3_lt6_id_ge6_rot2
x2
x0
)
(
ChurchNums_8_perm_2_3_4_5_6_7_0_1
x2
)
(
ChurchNums_8x3_to_3_lt6_id_ge6_rot2
x3
x1
)
(
ChurchNums_8_perm_2_3_4_5_6_7_0_1
x3
)
Param
ChurchNums_8x3_lt7_id_ge7_rot1
:
(
(
(
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
) →
CN (
ι
→
ι
)
Param
ChurchNums_8x3_to_3_lt7_id_ge7_rot2
:
(
(
(
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
) →
CN (
ι
→
ι
)
Known
1aa1c..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_to_3_lt7_id_ge7_rot2
x0
x1
)
Known
f8e90..
:
∀ 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
.
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_8ary_proj_p
x0
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_3ary_proj_p
(
ChurchNums_8x3_lt7_id_ge7_rot1
x0
x1
)
Known
dfbcd..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_to_3_lt7_id_ge7_rot2
x0
(
ChurchNums_8x3_lt7_id_ge7_rot1
x0
x1
)
=
x1
Known
e57bb..
:
∀ 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
⟶
∀ x1 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNums_8x3_lt7_id_ge7_rot1
x0
(
ChurchNums_8x3_to_3_lt7_id_ge7_rot2
x0
x1
)
=
x1
Known
eb832..
:
∀ 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_8x3_to_3_lt7_id_ge7_rot2
x2
x0
)
(
ChurchNums_8_perm_1_2_3_4_5_6_7_0
x2
)
(
ChurchNums_8x3_to_3_lt7_id_ge7_rot2
x3
x1
)
(
ChurchNums_8_perm_1_2_3_4_5_6_7_0
x3
)
Theorem
6fa76..
:
∀ 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_8ary_proj_p
x1
⟶
∀ x2 : ο .
(
∀ x3 x4 :
(
(
(
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
)
→
(
(
(
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
.
∀ x5 x6 :
(
(
(
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
)
→
(
(
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
.
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
x8
⟶
ChurchNum_3ary_proj_p
(
x3
x8
x7
)
)
⟶
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
x8
⟶
ChurchNum_3ary_proj_p
(
x4
x8
x7
)
)
⟶
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x8
⟶
x3
x8
(
x4
x8
x7
)
=
x7
)
⟶
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x8
⟶
x4
x8
(
x3
x8
x7
)
=
x7
)
⟶
(
∀ x7 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
(
x5
x7
)
)
⟶
(
∀ x7 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
(
x6
x7
)
)
⟶
(
∀ x7 :
(
(
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
.
x5
(
x6
x7
)
=
x7
)
⟶
(
∀ x7 :
(
(
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
.
x6
(
x5
x7
)
=
x7
)
⟶
(
∀ x7 x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x9 x10 :
(
(
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
x7
⟶
ChurchNum_3ary_proj_p
x8
⟶
ChurchNum_8ary_proj_p
x9
⟶
ChurchNum_8ary_proj_p
x10
⟶
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x7
x9
x8
x10
=
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
x3
x9
x7
)
(
x5
x9
)
(
x3
x10
x8
)
(
x5
x10
)
)
⟶
(
x5
x1
=
λ x8 x9 x10 x11 x12 x13 x14 x15 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
x2
)
⟶
x2
(proof)
Known
dca1b..
:
∀ x0 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x0
⟶
∀ x1 : ο .
(
∀ 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
.
(
∀ x4 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x4
⟶
ChurchNum_3ary_proj_p
(
x2
x4
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
ChurchNum_3ary_proj_p
x4
⟶
ChurchNum_3ary_proj_p
(
x3
x4
)
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x2
(
x3
x4
)
=
x4
)
⟶
(
∀ x4 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
x3
(
x2
x4
)
=
x4
)
⟶
(
∀ x4 x5 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x6 x7 :
(
(
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
.
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x4
x6
x5
x7
=
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
x2
x4
)
x6
(
x2
x5
)
x7
)
⟶
(
x2
x0
=
λ x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
⟶
x1
)
⟶
x1
Theorem
3c996..
:
∀ 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
⟶
∀ x2 : ο .
(
∀ x3 x4 :
(
(
(
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
)
→
(
(
(
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
.
∀ x5 x6 :
(
(
(
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
)
→
(
(
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
.
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
x8
⟶
ChurchNum_3ary_proj_p
(
x3
x8
x7
)
)
⟶
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
x8
⟶
ChurchNum_3ary_proj_p
(
x4
x8
x7
)
)
⟶
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x8
⟶
x3
x8
(
x4
x8
x7
)
=
x7
)
⟶
(
∀ x7 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x8 :
(
(
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
x8
⟶
x4
x8
(
x3
x8
x7
)
=
x7
)
⟶
(
∀ x7 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
(
x5
x7
)
)
⟶
(
∀ x7 :
(
(
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
x7
⟶
ChurchNum_8ary_proj_p
(
x6
x7
)
)
⟶
(
∀ x7 :
(
(
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
.
x5
(
x6
x7
)
=
x7
)
⟶
(
∀ x7 :
(
(
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
.
x6
(
x5
x7
)
=
x7
)
⟶
(
∀ x7 x8 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x9 x10 :
(
(
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
x7
⟶
ChurchNum_3ary_proj_p
x8
⟶
ChurchNum_8ary_proj_p
x9
⟶
ChurchNum_8ary_proj_p
x10
⟶
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x7
x9
x8
x10
=
TwoRamseyGraph_4_5_24_ChurchNums_3x8
(
x3
x9
x7
)
(
x5
x9
)
(
x3
x10
x8
)
(
x5
x10
)
)
⟶
(
x3
x1
x0
=
λ x8 x9 x10 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
(
x5
x1
=
λ x8 x9 x10 x11 x12 x13 x14 x15 :
(
ι → ι
)
→
ι → ι
.
x8
)
⟶
x2
)
⟶
x2
(proof)
Definition
False
False
:=
∀ x0 : ο .
x0
Definition
not
not
:=
λ x0 : ο .
x0
⟶
False
Definition
and
and
:=
λ x0 x1 : ο .
∀ x2 : ο .
(
x0
⟶
x1
⟶
x2
)
⟶
x2
Definition
ChurchNums_3x8_eq
:=
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
.
and
(
x0
=
x2
)
(
x1
=
x3
)
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)
Theorem
aa35a..
:
∀ x0 x1 x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ x4 x5 x6 x7 :
(
(
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_3ary_proj_p
x3
⟶
ChurchNum_8ary_proj_p
x4
⟶
ChurchNum_8ary_proj_p
x5
⟶
ChurchNum_8ary_proj_p
x6
⟶
ChurchNum_8ary_proj_p
x7
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x4
x1
x5
=
λ x9 x10 .
x9
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x4
x2
x6
=
λ x9 x10 .
x9
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x0
x4
x3
x7
=
λ x9 x10 .
x9
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x1
x5
x2
x6
=
λ x9 x10 .
x9
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x1
x5
x3
x7
=
λ x9 x10 .
x9
)
⟶
(
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x2
x6
x3
x7
=
λ x9 x10 .
x9
)
⟶
ChurchNums_3x8_neq
x0
x4
x1
x5
⟶
ChurchNums_3x8_neq
x0
x4
x2
x6
⟶
ChurchNums_3x8_neq
x0
x4
x3
x7
⟶
ChurchNums_3x8_neq
x1
x5
x2
x6
⟶
ChurchNums_3x8_neq
x1
x5
x3
x7
⟶
ChurchNums_3x8_neq
x2
x6
x3
x7
⟶
False
(proof)
Definition
Subq
Subq
:=
λ x0 x1 .
∀ x2 .
x2
∈
x0
⟶
x2
∈
x1
Param
u24
:
ι
Param
atleastp
atleastp
:
ι
→
ι
→
ο
Param
u4
:
ι
Param
ordsucc
ordsucc
:
ι
→
ι
Definition
TwoRamseyGraph_4_5_24
:=
λ x0 x1 .
∀ x2 x3 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ 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
x2
⟶
ChurchNum_3ary_proj_p
x3
⟶
ChurchNum_8ary_proj_p
x4
⟶
ChurchNum_8ary_proj_p
x5
⟶
x0
=
x2
(
λ x7 :
ι → ι
.
λ x8 .
x8
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
ordsucc
(
x4
(
λ x7 :
ι → ι
.
λ x8 .
x8
)
(
λ x7 :
ι → ι
.
x7
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
x8
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
x8
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
)
ordsucc
0
)
⟶
x1
=
x3
(
λ x7 :
ι → ι
.
λ x8 .
x8
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
ordsucc
(
x5
(
λ x7 :
ι → ι
.
λ x8 .
x8
)
(
λ x7 :
ι → ι
.
x7
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
x8
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
x8
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
(
λ x7 :
ι → ι
.
λ x8 .
x7
(
x7
(
x7
(
x7
(
x7
(
x7
(
x7
x8
)
)
)
)
)
)
)
ordsucc
0
)
⟶
TwoRamseyGraph_4_5_24_ChurchNums_3x8
x2
x4
x3
x5
=
λ x7 x8 .
x7
Known
d03c6..
:
∀ x0 .
atleastp
u4
x0
⟶
∀ x1 : ο .
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
(
x2
=
x3
⟶
∀ x6 : ο .
x6
)
⟶
(
x2
=
x4
⟶
∀ x6 : ο .
x6
)
⟶
(
x2
=
x5
⟶
∀ x6 : ο .
x6
)
⟶
(
x3
=
x4
⟶
∀ x6 : ο .
x6
)
⟶
(
x3
=
x5
⟶
∀ x6 : ο .
x6
)
⟶
(
x4
=
x5
⟶
∀ x6 : ο .
x6
)
⟶
x1
)
⟶
x1
Known
4f390..
:
∀ x0 .
x0
∈
u24
⟶
∀ x1 : ο .
(
∀ x2 :
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
(
ι → ι
)
→
ι → ι
)
→
(
ι → ι
)
→
ι → ι
.
∀ 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
x2
⟶
ChurchNum_8ary_proj_p
x3
⟶
x0
=
x2
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
x6
)
)
)
)
)
)
)
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
x6
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
ordsucc
(
x3
(
λ x5 :
ι → ι
.
λ x6 .
x6
)
(
λ x5 :
ι → ι
.
x5
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
x6
)
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
(
x5
x6
)
)
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
(
x5
(
x5
x6
)
)
)
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
(
x5
(
x5
(
x5
x6
)
)
)
)
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
(
x5
(
x5
(
x5
(
x5
x6
)
)
)
)
)
)
(
λ x5 :
ι → ι
.
λ x6 .
x5
(
x5
(
x5
(
x5
(
x5
(
x5
(
x5
x6
)
)
)
)
)
)
)
ordsucc
0
)
⟶
x1
)
⟶
x1
Theorem
51a60..
:
∀ x0 .
x0
⊆
u24
⟶
atleastp
u4
x0
⟶
not
(
∀ x1 .
x1
∈
x0
⟶
∀ x2 .
x2
∈
x0
⟶
(
x1
=
x2
⟶
∀ x3 : ο .
x3
)
⟶
TwoRamseyGraph_4_5_24
x1
x2
)
(proof)