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4ca31..
doc published by
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Definition
bb6a5..
:=
λ x0 x1 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
λ x2 x3 .
x0
(
x1
x3
x2
x2
x3
x3
x3
x3
x2
x3
x3
x2
x3
x3
x3
x3
x2
x3
)
(
x1
x2
x3
x3
x2
x3
x3
x2
x3
x3
x3
x3
x2
x2
x3
x3
x3
x3
)
(
x1
x2
x3
x3
x2
x3
x2
x3
x3
x2
x3
x3
x3
x3
x3
x2
x3
x3
)
(
x1
x3
x2
x2
x3
x2
x3
x3
x3
x3
x2
x3
x3
x3
x2
x3
x3
x3
)
(
x1
x3
x3
x3
x2
x3
x2
x2
x3
x3
x3
x2
x3
x3
x3
x3
x2
x3
)
(
x1
x3
x3
x2
x3
x2
x3
x3
x2
x3
x3
x3
x2
x2
x3
x3
x3
x3
)
(
x1
x3
x2
x3
x3
x2
x3
x3
x2
x2
x3
x3
x3
x3
x3
x2
x3
x3
)
(
x1
x2
x3
x3
x3
x3
x2
x2
x3
x3
x2
x3
x3
x3
x2
x3
x3
x3
)
(
x1
x3
x3
x2
x3
x3
x3
x2
x3
x3
x3
x3
x2
x2
x2
x3
x3
x3
)
(
x1
x3
x3
x3
x2
x3
x3
x3
x2
x3
x3
x2
x3
x2
x3
x3
x2
x3
)
(
x1
x2
x3
x3
x3
x2
x3
x3
x3
x3
x2
x3
x3
x3
x2
x2
x3
x3
)
(
x1
x3
x2
x3
x3
x3
x2
x3
x3
x2
x3
x3
x3
x3
x3
x2
x2
x3
)
(
x1
x3
x2
x3
x3
x3
x2
x3
x3
x2
x2
x3
x3
x3
x3
x3
x3
x2
)
(
x1
x3
x3
x3
x2
x3
x3
x3
x2
x2
x3
x2
x3
x3
x3
x3
x3
x2
)
(
x1
x3
x3
x2
x3
x3
x3
x2
x3
x3
x3
x2
x2
x3
x3
x3
x3
x2
)
(
x1
x2
x3
x3
x3
x2
x3
x3
x3
x3
x2
x3
x2
x3
x3
x3
x3
x2
)
(
x1
x3
x3
x3
x3
x3
x3
x3
x3
x3
x3
x3
x3
x2
x2
x2
x2
x3
)
Definition
Church17_p
:=
λ x0 :
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
)
→ ο
.
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x2
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x3
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x4
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x5
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x6
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x7
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x8
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x9
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x10
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x11
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x12
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x13
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x14
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x15
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x16
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x17
)
⟶
x1
(
λ x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 x18 .
x18
)
⟶
x1
x0
Definition
TwoRamseyGraph_3_6_Church17
:=
λ x0 x1 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
λ x2 x3 .
x0
(
x1
x2
x2
x2
x3
x3
x3
x3
x2
x3
x3
x2
x3
x3
x3
x3
x2
x3
)
(
x1
x2
x2
x3
x2
x3
x3
x2
x3
x3
x3
x3
x2
x2
x3
x3
x3
x3
)
(
x1
x2
x3
x2
x2
x3
x2
x3
x3
x2
x3
x3
x3
x3
x3
x2
x3
x3
)
(
x1
x3
x2
x2
x2
x2
x3
x3
x3
x3
x2
x3
x3
x3
x2
x3
x3
x3
)
(
x1
x3
x3
x3
x2
x2
x2
x2
x3
x3
x3
x2
x3
x3
x3
x3
x2
x3
)
(
x1
x3
x3
x2
x3
x2
x2
x3
x2
x3
x3
x3
x2
x2
x3
x3
x3
x3
)
(
x1
x3
x2
x3
x3
x2
x3
x2
x2
x2
x3
x3
x3
x3
x3
x2
x3
x3
)
(
x1
x2
x3
x3
x3
x3
x2
x2
x2
x3
x2
x3
x3
x3
x2
x3
x3
x3
)
(
x1
x3
x3
x2
x3
x3
x3
x2
x3
x2
x3
x3
x2
x2
x2
x3
x3
x3
)
(
x1
x3
x3
x3
x2
x3
x3
x3
x2
x3
x2
x2
x3
x2
x3
x3
x2
x3
)
(
x1
x2
x3
x3
x3
x2
x3
x3
x3
x3
x2
x2
x3
x3
x2
x2
x3
x3
)
(
x1
x3
x2
x3
x3
x3
x2
x3
x3
x2
x3
x3
x2
x3
x3
x2
x2
x3
)
(
x1
x3
x2
x3
x3
x3
x2
x3
x3
x2
x2
x3
x3
x2
x3
x3
x3
x2
)
(
x1
x3
x3
x3
x2
x3
x3
x3
x2
x2
x3
x2
x3
x3
x2
x3
x3
x2
)
(
x1
x3
x3
x2
x3
x3
x3
x2
x3
x3
x3
x2
x2
x3
x3
x2
x3
x2
)
(
x1
x2
x3
x3
x3
x2
x3
x3
x3
x3
x2
x3
x2
x3
x3
x3
x2
x2
)
(
x1
x3
x3
x3
x3
x3
x3
x3
x3
x3
x3
x3
x3
x2
x2
x2
x2
x2
)
Definition
False
False
:=
∀ x0 : ο .
x0
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Theorem
9b660..
:
∀ x0 x1 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
Church17_p
x0
⟶
Church17_p
x1
⟶
(
x0
=
x1
⟶
∀ x2 : ο .
x2
)
⟶
bb6a5..
x0
x1
=
TwoRamseyGraph_3_6_Church17
x0
x1
(proof)
Theorem
f28e7..
:
∀ x0 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
Church17_p
x0
⟶
bb6a5..
x0
x0
=
λ x2 x3 .
x3
(proof)
Theorem
9de19..
:
∀ x0 x1 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
Church17_p
x0
⟶
Church17_p
x1
⟶
bb6a5..
x0
x1
=
bb6a5..
x1
x0
(proof)
Param
u17
:
ι
Param
u17_to_Church17
:
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
Definition
e5bd5..
:=
λ x0 x1 .
x0
∈
u17
⟶
x1
∈
u17
⟶
bb6a5..
(
u17_to_Church17
x0
)
(
u17_to_Church17
x1
)
=
λ x3 x4 .
x3
Known
db165..
:
∀ x0 .
x0
∈
u17
⟶
Church17_p
(
u17_to_Church17
x0
)
Theorem
5445c..
:
∀ x0 x1 .
e5bd5..
x0
x1
⟶
e5bd5..
x1
x0
(proof)
Definition
Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
:=
λ x0 :
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 x9 x10 x11 x12 x13 x14 x15 x16 .
x0
x2
x4
x1
x3
x6
x8
x5
x7
x11
x9
x12
x10
x14
x15
x16
x13
Param
ordsucc
ordsucc
:
ι
→
ι
Definition
u1
:=
1
Definition
u2
:=
ordsucc
u1
Definition
u3
:=
ordsucc
u2
Definition
u4
:=
ordsucc
u3
Definition
u5
:=
ordsucc
u4
Definition
u6
:=
ordsucc
u5
Definition
u7
:=
ordsucc
u6
Definition
u8
:=
ordsucc
u7
Definition
u9
:=
ordsucc
u8
Definition
u10
:=
ordsucc
u9
Definition
u11
:=
ordsucc
u10
Definition
u12
:=
ordsucc
u11
Definition
u13
:=
ordsucc
u12
Definition
u14
:=
ordsucc
u13
Definition
u15
:=
ordsucc
u14
Definition
u16
:=
ordsucc
u15
Definition
Church17_to_u17
:=
λ x0 :
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι →
ι → ι
.
x0
0
u1
u2
u3
u4
u5
u6
u7
u8
u9
u10
u11
u12
u13
u14
u15
u16
Definition
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
:=
λ x0 .
Church17_to_u17
(
Church17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
(
u17_to_Church17
x0
)
)
Known
c5926..
:
u17_to_Church17
0
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x1
Theorem
428fd..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
0
=
u1
(proof)
Known
b0ce1..
:
u17_to_Church17
u1
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x2
Theorem
6eb3e..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u1
=
u3
(proof)
Known
e8ec5..
:
u17_to_Church17
u2
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x3
Theorem
00076..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u2
=
0
(proof)
Known
1ef08..
:
u17_to_Church17
u3
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x4
Theorem
737c8..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u3
=
u2
(proof)
Known
05513..
:
u17_to_Church17
u4
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x5
Theorem
b5b60..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u4
=
u5
(proof)
Known
22977..
:
u17_to_Church17
u5
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x6
Theorem
d3a23..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u5
=
u7
(proof)
Known
0e32a..
:
u17_to_Church17
u6
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x7
Theorem
9e037..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u6
=
u4
(proof)
Known
b0f83..
:
u17_to_Church17
u7
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x8
Theorem
af667..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u7
=
u6
(proof)
Known
48ba7..
:
u17_to_Church17
u8
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x9
Theorem
86df1..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u8
=
u10
(proof)
Known
a3fb1..
:
u17_to_Church17
u9
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x10
Theorem
1f384..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u9
=
u8
(proof)
Known
d7087..
:
u17_to_Church17
u10
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x11
Theorem
f964e..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u10
=
u11
(proof)
Known
a87a3..
:
u17_to_Church17
u11
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x12
Theorem
1f07b..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u11
=
u9
(proof)
Known
a52d8..
:
u17_to_Church17
u12
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x13
Theorem
be3a6..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u12
=
u13
(proof)
Known
0975c..
:
u17_to_Church17
u13
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x14
Theorem
0e84a..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u13
=
u14
(proof)
Known
cf897..
:
u17_to_Church17
u14
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x15
Theorem
4b6e2..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u14
=
u15
(proof)
Known
c424d..
:
u17_to_Church17
u15
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x16
Theorem
5681c..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u15
=
u12
(proof)
Known
480e6..
:
u17_to_Church17
u16
=
λ x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 x17 .
x17
Theorem
4c42e..
:
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
u16
=
u16
(proof)
Known
660da..
:
∀ x0 .
x0
∈
u16
⟶
∀ x1 :
ι → ο
.
x1
0
⟶
x1
u1
⟶
x1
u2
⟶
x1
u3
⟶
x1
u4
⟶
x1
u5
⟶
x1
u6
⟶
x1
u7
⟶
x1
u8
⟶
x1
u9
⟶
x1
u10
⟶
x1
u11
⟶
x1
u12
⟶
x1
u13
⟶
x1
u14
⟶
x1
u15
⟶
x1
x0
Known
6ec80..
:
1
∈
16
Known
f312e..
:
3
∈
16
Known
2c104..
:
0
∈
16
Known
b34ab..
:
2
∈
16
Known
fe610..
:
5
∈
16
Known
64265..
:
7
∈
16
Known
add3d..
:
4
∈
16
Known
6d5be..
:
6
∈
16
Known
662c8..
:
10
∈
16
Known
98f71..
:
8
∈
16
Known
2039c..
:
11
∈
16
Known
fdaf0..
:
9
∈
16
Known
e0b58..
:
13
∈
16
Known
d4076..
:
14
∈
16
Known
0e6a7..
:
15
∈
16
Known
be924..
:
12
∈
16
Theorem
f9dcb..
:
∀ x0 .
x0
∈
u16
⟶
u17_perm_1_3_0_2_5_7_4_6_10_8_11_9_13_14_15_12
x0
∈
u16
(proof)