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f4db5003f3e8843f870f2ff0273b2fd086f540c37ba5df9d63bb1573e2880674
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3d48a7adf85e8bba855e10f6fbee69c6cf7e3f9056220f6bc04aeb5f2fdd42d8
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18494
tx
d43b3..
preasset
doc published by
Pr4zB..
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
)
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
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
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
Known
cef55..
:
ChurchNum_3ary_proj_p
(
λ x0 x1 x2 :
(
ι → ι
)
→
ι → ι
.
x0
)
Known
a5963..
:
ChurchNum_3ary_proj_p
(
λ x0 x1 x2 :
(
ι → ι
)
→
ι → ι
.
x2
)
Known
18961..
:
ChurchNum_3ary_proj_p
(
λ x0 x1 x2 :
(
ι → ι
)
→
ι → ι
.
x1
)
Theorem
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
)
(proof)
Known
208f3..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x0
)
Known
7734d..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x7
)
Known
94187..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x6
)
Known
0ab9f..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x5
)
Known
3a83b..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x4
)
Known
446d8..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x3
)
Known
e5caa..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x2
)
Known
ef1ab..
:
ChurchNum_8ary_proj_p
(
λ x0 x1 x2 x3 x4 x5 x6 x7 :
(
ι → ι
)
→
ι → ι
.
x1
)
Theorem
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
)
(proof)
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
)
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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
)
)
)
)
(
x1
(
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
.
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
)
)
(
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
)
)
)
(
x2
(
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
)
)
(
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
)
)
)
(
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
.
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
)
)
(
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
)
)
)
(
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
.
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
)
)
(
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
)
)
)
(
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
)
Theorem
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
)
(proof)