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Proofgold Asset
asset id
3d79c07176ea788fa9ace27d44d85a5d0c8cc237118d39307a52d3b625a22467
asset hash
ee22bb492ccc814af86d523f403e3fd09963aa8af46a0c3a40c711f198f0efca
bday / block
18387
tx
e187f..
preasset
doc published by
Pr4zB..
Definition
ChurchNum_3ary_proj_p
:=
λ 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
)
→ ο
.
x1
(
λ x2 x3 x4 :
(
ι → ι
)
→
ι → ι
.
x2
)
⟶
x1
(
λ x2 x3 x4 :
(
ι → ι
)
→
ι → ι
.
x3
)
⟶
x1
(
λ x2 x3 x4 :
(
ι → ι
)
→
ι → ι
.
x4
)
⟶
x1
x0
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
)
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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
)
)
)
(
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
)
Known
d5994..
:
∀ x0 :
(
(
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
(
λ x1 x2 x3 :
(
ι → ι
)
→
ι → ι
.
x0
x3
x1
x2
)
Known
081ec..
:
∀ x0 :
(
(
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
(
λ x1 x2 x3 :
(
ι → ι
)
→
ι → ι
.
x0
x2
x3
x1
)
Theorem
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
(proof)
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
Definition
False
False
:=
∀ x0 : ο .
x0
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Known
768c1..
:
(
(
λ x1 x2 .
x2
)
=
λ x1 x2 .
x1
)
⟶
∀ x0 : ο .
x0
Theorem
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
(proof)