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Proofgold Asset
asset id
628d0056eaaee5e2352d50bc24a6a02e3e1be4aff3a3aa715fd4cd9862982b09
asset hash
93742d4351b3f808c6969c9b7a70a2d5bc2d6a1220d09f7d5b3495732fd70398
bday / block
18879
tx
299c6..
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
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
ordsucc
ordsucc
:
ι
→
ι
Definition
ChurchNums_3x8_to_u24
:=
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
.
x0
(
x1
(
λ x2 :
ι → ι
.
λ x3 .
x3
)
(
λ x2 :
ι → ι
.
x2
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
x3
)
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
(
x2
x3
)
)
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
(
x2
(
x2
x3
)
)
)
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
(
x2
(
x2
(
x2
x3
)
)
)
)
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
(
x2
(
x2
(
x2
(
x2
x3
)
)
)
)
)
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
x3
)
)
)
)
)
)
)
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x1
(
λ x4 :
ι → ι
.
λ x5 .
x5
)
(
λ x4 :
ι → ι
.
x4
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
x5
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
x5
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
)
)
)
x2
x3
)
)
)
)
)
)
)
)
)
(
λ x2 :
ι → ι
.
λ x3 .
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x2
(
x1
(
λ x4 :
ι → ι
.
λ x5 .
x5
)
(
λ x4 :
ι → ι
.
x4
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
x5
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
x5
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
)
)
(
λ x4 :
ι → ι
.
λ x5 .
x4
(
x4
(
x4
(
x4
(
x4
(
x4
(
x4
x5
)
)
)
)
)
)
)
x2
x3
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
)
ordsucc
0
Definition
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
:=
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 :
(
(
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
x3
x4
)
(
x1
x2
x3
x4
)
(
x1
x2
x3
x4
)
(
x1
x2
x3
x4
)
(
x1
x2
x3
x4
)
(
x1
x3
x4
x2
)
(
x1
x3
x4
x2
)
(
x1
x3
x4
x2
)
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
Param
and
and
:
ο
→
ο
→
ο
Definition
u1
:=
1
Definition
u2
:=
ordsucc
u1
Definition
u3
:=
ordsucc
u2
Known
neq_3_0
neq_3_0
:
u3
=
0
⟶
∀ x0 : ο .
x0
Known
neq_3_1
neq_3_1
:
u3
=
u1
⟶
∀ x0 : ο .
x0
Known
neq_3_2
neq_3_2
:
u3
=
u2
⟶
∀ x0 : ο .
x0
Definition
u4
:=
ordsucc
u3
Known
neq_4_3
neq_4_3
:
u4
=
u3
⟶
∀ x0 : ο .
x0
Definition
u5
:=
ordsucc
u4
Known
neq_5_3
neq_5_3
:
u5
=
u3
⟶
∀ x0 : ο .
x0
Definition
u6
:=
ordsucc
u5
Known
neq_6_3
neq_6_3
:
u6
=
u3
⟶
∀ x0 : ο .
x0
Definition
u7
:=
ordsucc
u6
Known
neq_7_3
neq_7_3
:
u7
=
u3
⟶
∀ x0 : ο .
x0
Definition
u8
:=
ordsucc
u7
Known
neq_8_3
neq_8_3
:
u8
=
u3
⟶
∀ x0 : ο .
x0
Definition
u9
:=
ordsucc
u8
Known
neq_9_3
neq_9_3
:
u9
=
u3
⟶
∀ x0 : ο .
x0
Definition
u10
:=
ordsucc
u9
Known
68152..
:
u10
=
u3
⟶
∀ x0 : ο .
x0
Definition
u11
:=
ordsucc
u10
Known
b06e1..
:
u11
=
u3
⟶
∀ x0 : ο .
x0
Definition
u12
:=
ordsucc
u11
Known
e015c..
:
u12
=
u3
⟶
∀ x0 : ο .
x0
Definition
u13
:=
ordsucc
u12
Known
19222..
:
u13
=
u3
⟶
∀ x0 : ο .
x0
Definition
u14
:=
ordsucc
u13
Known
d0fe4..
:
u14
=
u3
⟶
∀ x0 : ο .
x0
Definition
u15
:=
ordsucc
u14
Known
70124..
:
u15
=
u3
⟶
∀ x0 : ο .
x0
Definition
u16
:=
ordsucc
u15
Known
ca5c3..
:
u16
=
u3
⟶
∀ x0 : ο .
x0
Definition
u17
:=
ordsucc
u16
Known
6c299..
:
u17
=
u3
⟶
∀ x0 : ο .
x0
Definition
u18
:=
ordsucc
u17
Known
1f012..
:
u18
=
u3
⟶
∀ x0 : ο .
x0
Definition
u19
:=
ordsucc
u18
Known
2e7b7..
:
u19
=
u3
⟶
∀ x0 : ο .
x0
Definition
u20
:=
ordsucc
u19
Known
0af1b..
:
u20
=
u3
⟶
∀ x0 : ο .
x0
Definition
u21
:=
ordsucc
u20
Known
272ed..
:
u21
=
u3
⟶
∀ x0 : ο .
x0
Definition
u22
:=
ordsucc
u21
Known
17aea..
:
u22
=
u3
⟶
∀ x0 : ο .
x0
Definition
u23
:=
ordsucc
u22
Known
3d5c1..
:
u23
=
u3
⟶
∀ x0 : ο .
x0
Known
neq_4_0
neq_4_0
:
u4
=
0
⟶
∀ x0 : ο .
x0
Known
neq_4_1
neq_4_1
:
u4
=
u1
⟶
∀ x0 : ο .
x0
Known
neq_4_2
neq_4_2
:
u4
=
u2
⟶
∀ x0 : ο .
x0
Known
neq_5_4
neq_5_4
:
u5
=
u4
⟶
∀ x0 : ο .
x0
Known
neq_6_4
neq_6_4
:
u6
=
u4
⟶
∀ x0 : ο .
x0
Known
neq_7_4
neq_7_4
:
u7
=
u4
⟶
∀ x0 : ο .
x0
Known
neq_8_4
neq_8_4
:
u8
=
u4
⟶
∀ x0 : ο .
x0
Known
neq_9_4
neq_9_4
:
u9
=
u4
⟶
∀ x0 : ο .
x0
Known
33d16..
:
u10
=
u4
⟶
∀ x0 : ο .
x0
Known
6a6f1..
:
u11
=
u4
⟶
∀ x0 : ο .
x0
Known
7aa79..
:
u12
=
u4
⟶
∀ x0 : ο .
x0
Known
4d850..
:
u13
=
u4
⟶
∀ x0 : ο .
x0
Known
ffd62..
:
u14
=
u4
⟶
∀ x0 : ο .
x0
Known
4b742..
:
u15
=
u4
⟶
∀ x0 : ο .
x0
Known
7b2eb..
:
u16
=
u4
⟶
∀ x0 : ο .
x0
Known
506a9..
:
u17
=
u4
⟶
∀ x0 : ο .
x0
Known
60e5c..
:
u18
=
u4
⟶
∀ x0 : ο .
x0
Known
26e28..
:
u19
=
u4
⟶
∀ x0 : ο .
x0
Known
f2a22..
:
u20
=
u4
⟶
∀ x0 : ο .
x0
Known
ac7ac..
:
u21
=
u4
⟶
∀ x0 : ο .
x0
Known
7f2f2..
:
u22
=
u4
⟶
∀ x0 : ο .
x0
Known
7d70a..
:
u23
=
u4
⟶
∀ x0 : ο .
x0
Known
neq_5_0
neq_5_0
:
u5
=
0
⟶
∀ x0 : ο .
x0
Known
neq_5_1
neq_5_1
:
u5
=
u1
⟶
∀ x0 : ο .
x0
Known
neq_5_2
neq_5_2
:
u5
=
u2
⟶
∀ x0 : ο .
x0
Known
neq_6_5
neq_6_5
:
u6
=
u5
⟶
∀ x0 : ο .
x0
Known
neq_7_5
neq_7_5
:
u7
=
u5
⟶
∀ x0 : ο .
x0
Known
neq_8_5
neq_8_5
:
u8
=
u5
⟶
∀ x0 : ο .
x0
Known
neq_9_5
neq_9_5
:
u9
=
u5
⟶
∀ x0 : ο .
x0
Known
a7d50..
:
u10
=
u5
⟶
∀ x0 : ο .
x0
Known
1b659..
:
u11
=
u5
⟶
∀ x0 : ο .
x0
Known
07eba..
:
u12
=
u5
⟶
∀ x0 : ο .
x0
Known
29333..
:
u13
=
u5
⟶
∀ x0 : ο .
x0
Known
d6c57..
:
u14
=
u5
⟶
∀ x0 : ο .
x0
Known
24fad..
:
u15
=
u5
⟶
∀ x0 : ο .
x0
Known
35bff..
:
u16
=
u5
⟶
∀ x0 : ο .
x0
Known
4ab36..
:
u17
=
u5
⟶
∀ x0 : ο .
x0
Known
ac512..
:
u18
=
u5
⟶
∀ x0 : ο .
x0
Known
dcd9d..
:
u19
=
u5
⟶
∀ x0 : ο .
x0
Known
98620..
:
u20
=
u5
⟶
∀ x0 : ο .
x0
Known
18fbb..
:
u21
=
u5
⟶
∀ x0 : ο .
x0
Known
9a712..
:
u22
=
u5
⟶
∀ x0 : ο .
x0
Known
b1d7f..
:
u23
=
u5
⟶
∀ x0 : ο .
x0
Known
neq_6_0
neq_6_0
:
u6
=
0
⟶
∀ x0 : ο .
x0
Known
neq_6_1
neq_6_1
:
u6
=
u1
⟶
∀ x0 : ο .
x0
Known
neq_6_2
neq_6_2
:
u6
=
u2
⟶
∀ x0 : ο .
x0
Known
neq_7_6
neq_7_6
:
u7
=
u6
⟶
∀ x0 : ο .
x0
Known
neq_8_6
neq_8_6
:
u8
=
u6
⟶
∀ x0 : ο .
x0
Known
neq_9_6
neq_9_6
:
u9
=
u6
⟶
∀ x0 : ο .
x0
Known
d0401..
:
u10
=
u6
⟶
∀ x0 : ο .
x0
Known
949f2..
:
u11
=
u6
⟶
∀ x0 : ο .
x0
Known
0bd83..
:
u12
=
u6
⟶
∀ x0 : ο .
x0
Known
02f5c..
:
u13
=
u6
⟶
∀ x0 : ο .
x0
Known
62d80..
:
u14
=
u6
⟶
∀ x0 : ο .
x0
Known
f5ac7..
:
u15
=
u6
⟶
∀ x0 : ο .
x0
Known
3bd28..
:
u16
=
u6
⟶
∀ x0 : ο .
x0
Known
b74f3..
:
u17
=
u6
⟶
∀ x0 : ο .
x0
Known
8347f..
:
u18
=
u6
⟶
∀ x0 : ο .
x0
Known
b1809..
:
u19
=
u6
⟶
∀ x0 : ο .
x0
Known
fd91d..
:
u20
=
u6
⟶
∀ x0 : ο .
x0
Known
2ec13..
:
u21
=
u6
⟶
∀ x0 : ο .
x0
Known
f4b67..
:
u22
=
u6
⟶
∀ x0 : ο .
x0
Known
51d86..
:
u23
=
u6
⟶
∀ x0 : ο .
x0
Known
neq_7_0
neq_7_0
:
u7
=
0
⟶
∀ x0 : ο .
x0
Known
neq_7_1
neq_7_1
:
u7
=
u1
⟶
∀ x0 : ο .
x0
Known
neq_7_2
neq_7_2
:
u7
=
u2
⟶
∀ x0 : ο .
x0
Known
neq_8_7
neq_8_7
:
u8
=
u7
⟶
∀ x0 : ο .
x0
Known
neq_9_7
neq_9_7
:
u9
=
u7
⟶
∀ x0 : ο .
x0
Known
7d7a8..
:
u10
=
u7
⟶
∀ x0 : ο .
x0
Known
4abfa..
:
u11
=
u7
⟶
∀ x0 : ο .
x0
Known
6a15f..
:
u12
=
u7
⟶
∀ x0 : ο .
x0
Known
d9b35..
:
u13
=
u7
⟶
∀ x0 : ο .
x0
Known
01bf6..
:
u14
=
u7
⟶
∀ x0 : ο .
x0
Known
008b1..
:
u15
=
u7
⟶
∀ x0 : ο .
x0
Known
d3a2f..
:
u16
=
u7
⟶
∀ x0 : ο .
x0
Known
66c81..
:
u17
=
u7
⟶
∀ x0 : ο .
x0
Known
c9d3b..
:
u18
=
u7
⟶
∀ x0 : ο .
x0
Known
36989..
:
u19
=
u7
⟶
∀ x0 : ο .
x0
Known
ae219..
:
u20
=
u7
⟶
∀ x0 : ο .
x0
Known
471c9..
:
u21
=
u7
⟶
∀ x0 : ο .
x0
Known
362ec..
:
u22
=
u7
⟶
∀ x0 : ο .
x0
Known
49af3..
:
u23
=
u7
⟶
∀ x0 : ο .
x0
Known
neq_8_0
neq_8_0
:
u8
=
0
⟶
∀ x0 : ο .
x0
Known
neq_8_1
neq_8_1
:
u8
=
u1
⟶
∀ x0 : ο .
x0
Known
neq_8_2
neq_8_2
:
u8
=
u2
⟶
∀ x0 : ο .
x0
Known
neq_9_8
neq_9_8
:
u9
=
u8
⟶
∀ x0 : ο .
x0
Known
96175..
:
u10
=
u8
⟶
∀ x0 : ο .
x0
Known
b3a20..
:
u11
=
u8
⟶
∀ x0 : ο .
x0
Known
a6a6c..
:
u12
=
u8
⟶
∀ x0 : ο .
x0
Known
0b225..
:
u13
=
u8
⟶
∀ x0 : ο .
x0
Known
4f6ad..
:
u14
=
u8
⟶
∀ x0 : ο .
x0
Known
c0d75..
:
u15
=
u8
⟶
∀ x0 : ο .
x0
Known
6c306..
:
u16
=
u8
⟶
∀ x0 : ο .
x0
Known
dc9e6..
:
u17
=
u8
⟶
∀ x0 : ο .
x0
Known
d47e8..
:
u18
=
u8
⟶
∀ x0 : ο .
x0
Known
9b462..
:
u19
=
u8
⟶
∀ x0 : ο .
x0
Known
54bdc..
:
u20
=
u8
⟶
∀ x0 : ο .
x0
Known
ada11..
:
u21
=
u8
⟶
∀ x0 : ο .
x0
Known
9d557..
:
u22
=
u8
⟶
∀ x0 : ο .
x0
Known
b0bcb..
:
u23
=
u8
⟶
∀ x0 : ο .
x0
Known
neq_9_0
neq_9_0
:
u9
=
0
⟶
∀ x0 : ο .
x0
Known
neq_9_1
neq_9_1
:
u9
=
u1
⟶
∀ x0 : ο .
x0
Known
neq_9_2
neq_9_2
:
u9
=
u2
⟶
∀ x0 : ο .
x0
Known
4fc31..
:
u10
=
u9
⟶
∀ x0 : ο .
x0
Known
4f03f..
:
u11
=
u9
⟶
∀ x0 : ο .
x0
Known
22885..
:
u12
=
u9
⟶
∀ x0 : ο .
x0
Known
3f24c..
:
u13
=
u9
⟶
∀ x0 : ο .
x0
Known
d7730..
:
u14
=
u9
⟶
∀ x0 : ο .
x0
Known
3a7bc..
:
u15
=
u9
⟶
∀ x0 : ο .
x0
Known
78b49..
:
u16
=
u9
⟶
∀ x0 : ο .
x0
Known
66dfd..
:
u17
=
u9
⟶
∀ x0 : ο .
x0
Known
d3922..
:
u18
=
u9
⟶
∀ x0 : ο .
x0
Known
4545d..
:
u19
=
u9
⟶
∀ x0 : ο .
x0
Known
6bb84..
:
u20
=
u9
⟶
∀ x0 : ο .
x0
Known
f159f..
:
u21
=
u9
⟶
∀ x0 : ο .
x0
Known
ac02b..
:
u22
=
u9
⟶
∀ x0 : ο .
x0
Known
b0849..
:
u23
=
u9
⟶
∀ x0 : ο .
x0
Known
0e10e..
:
u10
=
0
⟶
∀ x0 : ο .
x0
Known
d183f..
:
u10
=
u1
⟶
∀ x0 : ο .
x0
Known
e02d9..
:
u10
=
u2
⟶
∀ x0 : ο .
x0
Known
ebfb7..
:
u11
=
u10
⟶
∀ x0 : ο .
x0
Known
6c583..
:
u12
=
u10
⟶
∀ x0 : ο .
x0
Known
78358..
:
u13
=
u10
⟶
∀ x0 : ο .
x0
Known
f5ab5..
:
u14
=
u10
⟶
∀ x0 : ο .
x0
Known
b7f53..
:
u15
=
u10
⟶
∀ x0 : ο .
x0
Known
6879f..
:
u16
=
u10
⟶
∀ x0 : ο .
x0
Known
2e5d5..
:
u17
=
u10
⟶
∀ x0 : ο .
x0
Known
a335e..
:
u18
=
u10
⟶
∀ x0 : ο .
x0
Known
7d160..
:
u19
=
u10
⟶
∀ x0 : ο .
x0
Known
8b01c..
:
u20
=
u10
⟶
∀ x0 : ο .
x0
Known
b1234..
:
u21
=
u10
⟶
∀ x0 : ο .
x0
Known
4d4dd..
:
u22
=
u10
⟶
∀ x0 : ο .
x0
Known
b7dd9..
:
u23
=
u10
⟶
∀ x0 : ο .
x0
Known
19f75..
:
u11
=
0
⟶
∀ x0 : ο .
x0
Known
618f7..
:
u11
=
u1
⟶
∀ x0 : ο .
x0
Known
2c42c..
:
u11
=
u2
⟶
∀ x0 : ο .
x0
Known
ab306..
:
u12
=
u11
⟶
∀ x0 : ο .
x0
Known
bf497..
:
u13
=
u11
⟶
∀ x0 : ο .
x0
Known
4e1aa..
:
u14
=
u11
⟶
∀ x0 : ο .
x0
Known
9c5db..
:
u15
=
u11
⟶
∀ x0 : ο .
x0
Known
22184..
:
u16
=
u11
⟶
∀ x0 : ο .
x0
Known
454a8..
:
u17
=
u11
⟶
∀ x0 : ο .
x0
Known
8da43..
:
u18
=
u11
⟶
∀ x0 : ο .
x0
Known
8109a..
:
u19
=
u11
⟶
∀ x0 : ο .
x0
Known
66622..
:
u20
=
u11
⟶
∀ x0 : ο .
x0
Known
4c4e0..
:
u21
=
u11
⟶
∀ x0 : ο .
x0
Known
2051a..
:
u22
=
u11
⟶
∀ x0 : ο .
x0
Known
258a9..
:
u23
=
u11
⟶
∀ x0 : ο .
x0
Known
efdfc..
:
u12
=
0
⟶
∀ x0 : ο .
x0
Known
ce0cd..
:
u12
=
u1
⟶
∀ x0 : ο .
x0
Known
8158b..
:
u12
=
u2
⟶
∀ x0 : ο .
x0
Known
ad02f..
:
u13
=
u12
⟶
∀ x0 : ο .
x0
Known
ef4da..
:
u14
=
u12
⟶
∀ x0 : ο .
x0
Known
72647..
:
u15
=
u12
⟶
∀ x0 : ο .
x0
Known
fa664..
:
u16
=
u12
⟶
∀ x0 : ο .
x0
Known
9a69f..
:
u17
=
u12
⟶
∀ x0 : ο .
x0
Known
c1bd9..
:
u18
=
u12
⟶
∀ x0 : ο .
x0
Known
a5243..
:
u19
=
u12
⟶
∀ x0 : ο .
x0
Known
01bb6..
:
u20
=
u12
⟶
∀ x0 : ο .
x0
Known
6371d..
:
u21
=
u12
⟶
∀ x0 : ο .
x0
Known
db21d..
:
u22
=
u12
⟶
∀ x0 : ο .
x0
Known
3982c..
:
u23
=
u12
⟶
∀ x0 : ο .
x0
Known
733b2..
:
u13
=
0
⟶
∀ x0 : ο .
x0
Known
16246..
:
u13
=
u1
⟶
∀ x0 : ο .
x0
Known
40d25..
:
u13
=
u2
⟶
∀ x0 : ο .
x0
Known
e1947..
:
u14
=
u13
⟶
∀ x0 : ο .
x0
Known
4d8d4..
:
u15
=
u13
⟶
∀ x0 : ο .
x0
Known
4326e..
:
u16
=
u13
⟶
∀ x0 : ο .
x0
Known
30174..
:
u17
=
u13
⟶
∀ x0 : ο .
x0
Known
5cb8a..
:
u18
=
u13
⟶
∀ x0 : ο .
x0
Known
8c598..
:
u19
=
u13
⟶
∀ x0 : ο .
x0
Known
551bd..
:
u20
=
u13
⟶
∀ x0 : ο .
x0
Known
87a9a..
:
u21
=
u13
⟶
∀ x0 : ο .
x0
Known
6a662..
:
u22
=
u13
⟶
∀ x0 : ο .
x0
Known
4e72c..
:
u23
=
u13
⟶
∀ x0 : ο .
x0
Known
fc551..
:
u14
=
0
⟶
∀ x0 : ο .
x0
Known
ac679..
:
u14
=
u1
⟶
∀ x0 : ο .
x0
Known
0bb18..
:
u14
=
u2
⟶
∀ x0 : ο .
x0
Known
b8e82..
:
u15
=
u14
⟶
∀ x0 : ο .
x0
Known
71c5e..
:
u16
=
u14
⟶
∀ x0 : ο .
x0
Known
82608..
:
u17
=
u14
⟶
∀ x0 : ο .
x0
Known
d92fd..
:
u18
=
u14
⟶
∀ x0 : ο .
x0
Known
35149..
:
u19
=
u14
⟶
∀ x0 : ο .
x0
Known
28d21..
:
u20
=
u14
⟶
∀ x0 : ο .
x0
Known
25d09..
:
u21
=
u14
⟶
∀ x0 : ο .
x0
Known
bd746..
:
u22
=
u14
⟶
∀ x0 : ο .
x0
Known
ef472..
:
u23
=
u14
⟶
∀ x0 : ο .
x0
Known
160ad..
:
u15
=
0
⟶
∀ x0 : ο .
x0
Known
174d1..
:
u15
=
u1
⟶
∀ x0 : ο .
x0
Known
4d715..
:
u15
=
u2
⟶
∀ x0 : ο .
x0
Known
41073..
:
u16
=
u15
⟶
∀ x0 : ο .
x0
Known
ac12b..
:
u17
=
u15
⟶
∀ x0 : ο .
x0
Known
dfba1..
:
u18
=
u15
⟶
∀ x0 : ο .
x0
Known
38ccc..
:
u19
=
u15
⟶
∀ x0 : ο .
x0
Known
bf7ce..
:
u20
=
u15
⟶
∀ x0 : ο .
x0
Known
17bc6..
:
u21
=
u15
⟶
∀ x0 : ο .
x0
Known
ac3f7..
:
u22
=
u15
⟶
∀ x0 : ο .
x0
Known
eff68..
:
u23
=
u15
⟶
∀ x0 : ο .
x0
Known
86ae3..
:
u16
=
0
⟶
∀ x0 : ο .
x0
Known
ab690..
:
u16
=
u1
⟶
∀ x0 : ο .
x0
Known
296ac..
:
u16
=
u2
⟶
∀ x0 : ο .
x0
Known
7fbc8..
:
u17
=
u16
⟶
∀ x0 : ο .
x0
Known
0eaf4..
:
u18
=
u16
⟶
∀ x0 : ο .
x0
Known
0384c..
:
u19
=
u16
⟶
∀ x0 : ο .
x0
Known
996e8..
:
u20
=
u16
⟶
∀ x0 : ο .
x0
Known
39009..
:
u21
=
u16
⟶
∀ x0 : ο .
x0
Known
e7d80..
:
u22
=
u16
⟶
∀ x0 : ο .
x0
Known
c26ad..
:
u23
=
u16
⟶
∀ x0 : ο .
x0
Known
fcaf7..
:
u17
=
0
⟶
∀ x0 : ο .
x0
Known
d4359..
:
u17
=
u1
⟶
∀ x0 : ο .
x0
Known
2c536..
:
u17
=
u2
⟶
∀ x0 : ο .
x0
Known
82c6a..
:
u18
=
u17
⟶
∀ x0 : ο .
x0
Known
3c054..
:
u19
=
u17
⟶
∀ x0 : ο .
x0
Known
9ce5b..
:
u20
=
u17
⟶
∀ x0 : ο .
x0
Known
b821e..
:
u21
=
u17
⟶
∀ x0 : ο .
x0
Known
d3e26..
:
u22
=
u17
⟶
∀ x0 : ο .
x0
Known
e9a91..
:
u23
=
u17
⟶
∀ x0 : ο .
x0
Known
99743..
:
u18
=
0
⟶
∀ x0 : ο .
x0
Known
9ccac..
:
u18
=
u1
⟶
∀ x0 : ο .
x0
Known
ad866..
:
u18
=
u2
⟶
∀ x0 : ο .
x0
Known
97eb4..
:
u19
=
u18
⟶
∀ x0 : ο .
x0
Known
75fad..
:
u20
=
u18
⟶
∀ x0 : ο .
x0
Known
80a82..
:
u21
=
u18
⟶
∀ x0 : ο .
x0
Known
7957c..
:
u22
=
u18
⟶
∀ x0 : ο .
x0
Known
3bccb..
:
u23
=
u18
⟶
∀ x0 : ο .
x0
Known
fd18a..
:
u19
=
0
⟶
∀ x0 : ο .
x0
Known
70279..
:
u19
=
u1
⟶
∀ x0 : ο .
x0
Known
81672..
:
u19
=
u2
⟶
∀ x0 : ο .
x0
Known
2615b..
:
u20
=
u19
⟶
∀ x0 : ο .
x0
Known
44711..
:
u21
=
u19
⟶
∀ x0 : ο .
x0
Known
b0147..
:
u22
=
u19
⟶
∀ x0 : ο .
x0
Known
ad532..
:
u23
=
u19
⟶
∀ x0 : ο .
x0
Known
4552b..
:
u20
=
0
⟶
∀ x0 : ο .
x0
Known
d8b53..
:
u20
=
u1
⟶
∀ x0 : ο .
x0
Known
c9329..
:
u20
=
u2
⟶
∀ x0 : ο .
x0
Known
32e25..
:
u21
=
u20
⟶
∀ x0 : ο .
x0
Known
c8ac0..
:
u22
=
u20
⟶
∀ x0 : ο .
x0
Known
94779..
:
u23
=
u20
⟶
∀ x0 : ο .
x0
Known
1158c..
:
u21
=
0
⟶
∀ x0 : ο .
x0
Known
db0cd..
:
u21
=
u1
⟶
∀ x0 : ο .
x0
Known
ebee4..
:
u21
=
u2
⟶
∀ x0 : ο .
x0
Known
41315..
:
u22
=
u21
⟶
∀ x0 : ο .
x0
Known
1a616..
:
u23
=
u21
⟶
∀ x0 : ο .
x0
Known
e8714..
:
u22
=
0
⟶
∀ x0 : ο .
x0
Known
9e7b1..
:
u22
=
u1
⟶
∀ x0 : ο .
x0
Known
af720..
:
u22
=
u2
⟶
∀ x0 : ο .
x0
Known
3105f..
:
u23
=
u22
⟶
∀ x0 : ο .
x0
Known
c432c..
:
u23
=
0
⟶
∀ x0 : ο .
x0
Known
13d86..
:
u23
=
u1
⟶
∀ x0 : ο .
x0
Known
60a3a..
:
u23
=
u2
⟶
∀ x0 : ο .
x0
Known
neq_1_0
neq_1_0
:
u1
=
0
⟶
∀ x0 : ο .
x0
Known
neq_2_0
neq_2_0
:
u2
=
0
⟶
∀ x0 : ο .
x0
Known
neq_2_1
neq_2_1
:
u2
=
u1
⟶
∀ x0 : ο .
x0
Definition
False
False
:=
∀ x0 : ο .
x0
Known
FalseE
FalseE
:
False
⟶
∀ x0 : ο .
x0
Known
andI
andI
:
∀ x0 x1 : ο .
x0
⟶
x1
⟶
and
x0
x1
Theorem
85ac5..
:
∀ 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_8ary_proj_p
x2
⟶
ChurchNum_3ary_proj_p
x1
⟶
ChurchNum_8ary_proj_p
x3
⟶
ChurchNums_3x8_to_u24
(
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
x2
x0
)
(
ChurchNums_8_perm_3_4_5_6_7_0_1_2
x2
)
=
ChurchNums_3x8_to_u24
x1
x3
⟶
and
(
x1
=
ChurchNums_8x3_to_3_lt5_id_ge5_rot2
x2
x0
)
(
x3
=
ChurchNums_8_perm_3_4_5_6_7_0_1_2
x2
)
(proof)