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Proofgold Asset
asset id
35a8b2a898b7fc92f01e8ea78e3e70edcd0b209e03b35c886d22edb7267161e0
asset hash
233041d8e255aa27902ba1ffd59c2dfd23c8243081c2ff6e2fc6dee19ccf98e4
bday / block
39322
tx
6a372..
preasset
doc published by
Pr4zB..
Param
4006a..
:
(
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Param
fc090..
:
(
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) →
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ο
Param
07c0f..
:
(
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) →
ι
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ο
Param
0076f..
:
(
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ο
) →
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ο
Param
adf05..
:
(
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) →
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ο
Param
d5d69..
:
(
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) →
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ο
Param
3f98b..
:
(
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ο
) →
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ο
Param
96c31..
:
(
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) →
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ο
Param
54c7d..
:
(
ι
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ο
) →
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ο
Param
130d9..
:
(
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) →
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ο
Param
4e6fe..
:
(
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ο
) →
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→
ο
Param
a62c3..
:
(
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) →
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→
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→
ο
Param
ceccf..
:
(
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ο
) →
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ο
Param
eb506..
:
(
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ο
) →
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→
ι
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ι
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ι
→
ι
→
ο
Param
70755..
:
(
ι
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ο
) →
ι
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→
ι
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→
ο
Param
97793..
:
(
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) →
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→
ι
→
ι
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→
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→
ο
Param
aa64f..
:
(
ι
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→
ο
) →
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→
ι
→
ι
→
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→
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→
ο
Param
83aec..
:
(
ι
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→
ο
) →
ι
→
ι
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→
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ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
446f4..
:
(
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→
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) →
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→
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→
ι
→
ι
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ι
→
ι
→
ο
Param
ba015..
:
(
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) →
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ι
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ι
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ι
→
ο
Param
286f8..
:
(
ι
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→
ο
) →
ι
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ι
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ι
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→
ι
→
ι
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→
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→
ο
Param
2c550..
:
(
ι
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→
ο
) →
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→
ι
→
ι
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→
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→
ο
Param
f842a..
:
(
ι
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ο
) →
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ι
→
ι
→
ι
→
ι
→
ι
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ι
→
ι
→
ο
Param
e9fc9..
:
(
ι
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→
ο
) →
ι
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ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
010eb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fa0f3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c7001..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
58722..
:
(
ι
→
ι
→
ο
) →
ι
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→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
84d91..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
90d0e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
81d98..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
30a11..
:
(
ι
→
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→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
076b3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3d3e7..
:
(
ι
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ο
) →
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ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
14be0..
:
(
ι
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→
ο
) →
ι
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→
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→
ι
→
ι
→
ι
→
ι
→
ο
Param
4e91d..
:
(
ι
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→
ο
) →
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→
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ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
23b40..
:
(
ι
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→
ο
) →
ι
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→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1a9fd..
:
(
ι
→
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→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e2ec9..
:
(
ι
→
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→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c480f..
:
(
ι
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ο
) →
ι
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ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0db75..
:
(
ι
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→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
02471..
:
(
ι
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ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1cf57..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
23926..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b19dd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2eb4b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bce5f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
73f36..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
94ee4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
811c0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
96162..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0768d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
70a3c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2122d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
39c17..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ee5b5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
61b2a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
abda1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
858d1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
22b3a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
723e0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1ecf8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
915dd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
58208..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b571f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7e5de..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a3794..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
093ca..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
34ae8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
65996..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
45286..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b7a83..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
72d65..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b7e1a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4b4dd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f4940..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
682ac..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
5f6ee..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a2b8b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e2fd7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
05a8c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f5da9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
de118..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b43ab..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
627df..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c2e8a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
aa358..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
093ad..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bacd8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2bb2a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
803e1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f9a67..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
76a6c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7f17b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cc7e8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3a6bc..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ad740..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9aef0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
30182..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d2a2c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a94a5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
92dea..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8be9f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4e4f8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
37e04..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f7902..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ab042..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a2064..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8c9ed..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ee649..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
61fc8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ed012..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d68bd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d0e1f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1e021..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
989b4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6e051..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d92ce..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e5063..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
228c9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a3e51..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c705c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
38793..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e13e5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ef237..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3c50c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
7cafd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
72e0a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a4abc..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a40ae..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b1702..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f444d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
55a3e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8c70b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
17819..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
53f52..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
07fce..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
86fe8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fb47b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
055d9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
13b7c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2bf4d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cf078..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a0d70..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2e1d5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
729bd..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e1aab..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
241b0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8fbce..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6661c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a9907..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
824ef..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8f55d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
22bb5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
654b9..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
53286..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b8d2a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e5024..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f0823..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
62e18..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
49901..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
dc830..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ed1c7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
df50d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
176ba..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9f93b..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
91ca0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
23b03..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
00b44..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
62e18..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
49901..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
dc830..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
ed1c7..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
df50d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
176ba..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
9f93b..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
91ca0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
23b03..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
496a0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2ffc8..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e8ba7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b4c31..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1a9c5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bfd4f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d0980..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
bc2c6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
66709..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
496a0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
2ffc8..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
e8ba7..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
b4c31..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
1a9c5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
bfd4f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
d0980..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
bc2c6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
06d7e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b0749..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
87273..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b0e38..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f3db6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
21189..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
aad31..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
1a9c5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
06d7e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
b0749..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
496a0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
87273..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
b0e38..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
f3db6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
21189..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
d0e7c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f630d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9a66e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
93f0f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
2dac5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
3fca5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ef324..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
4ee07..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
d0e7c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
f630d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
9a66e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
93f0f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
2dac5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
bfd4f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
3fca5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
ef324..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
c4d5c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
dcb32..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
d3618..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
dbf71..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
e37fb..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
78a44..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
af5b6..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
ba478..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
c4d5c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
dcb32..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
d3618..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
dbf71..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
e37fb..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
78a44..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
af5b6..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
a7e88..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
59632..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
79ee1..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
f6312..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
fa2d0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
a1298..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
78a44..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
c4d5c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
a7e88..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
59632..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
79ee1..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
f6312..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
fa2d0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
dd43e..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4818f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4d3d7..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
a1497..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
4086f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
0d367..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
dd43e..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
4818f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
4d3d7..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
a1497..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
4086f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
44916..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
8acce..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
b47d4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
74622..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
0788d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
5963b..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
44916..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
8acce..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
b47d4..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
74622..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
0788d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
fa661..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
255f4..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
c8a3f..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
0a634..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
74622..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
fa661..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
44916..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
255f4..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
c8a3f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
2bad0..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
2feec..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
0788d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
2bad0..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
fa661..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
44916..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
c8a3f..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
d2e51..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
76e3a..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
9eede..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
ba960..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
74a95..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
465a4..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
d2e51..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
76e3a..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
9eede..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
ba960..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
74a95..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
59a16..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
94f0c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
923e2..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
1b69c..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
cec27..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
24cfd..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
59a16..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
94f0c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
923e2..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
1b69c..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
cec27..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
889b5..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
71ae3..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
df026..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
6bc75..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Param
43a9d..
:
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ι
→
ο
Definition
216e5..
:=
λ x0 .
λ x1 :
ι →
ι → ο
.
∀ x2 : ο .
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
889b5..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
71ae3..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
df026..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
6bc75..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
(
∀ x3 .
x3
∈
x0
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
43a9d..
x1
x3
x4
x5
x6
x7
x8
x9
x10
x11
⟶
x2
)
⟶
x2
Param
4402e..
:
ι
→
(
ι
→
ι
→
ο
) →
ο
Param
cf2df..
:
ι
→
(
ι
→
ι
→
ο
) →
ο
Param
Subq
Subq
:
ι
→
ι
→
ο
Param
setminus
setminus
:
ι
→
ι
→
ι
Param
Sing
Sing
:
ι
→
ι
Param
5bab1..
:
ι
→
(
ι
→
ι
→
ο
) →
ο
Known
70d6f..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
4006a..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
5e8a4..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
fc090..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
629c2..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
07c0f..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
58605..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
0076f..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
176e1..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
adf05..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
13c6c..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
d5d69..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
158a2..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
3f98b..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
0a416..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
96c31..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
3d567..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
54c7d..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
be036..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
130d9..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
6110e..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
4e6fe..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
1b89c..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
a62c3..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
bf274..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
ceccf..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
d3d64..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
eb506..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
79b20..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
70755..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
86d7f..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
97793..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
4ee2c..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
aa64f..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
53ca8..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
83aec..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
7cfa2..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
446f4..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
75ae5..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
496a0..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
774bc..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
2ffc8..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
128ce..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
e8ba7..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
22120..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
b4c31..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
d08d7..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
1a9c5..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
8fa6b..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
bfd4f..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
9ce91..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
d0980..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
09417..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
bc2c6..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
a96e6..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
66709..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
e9a54..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
06d7e..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
947d7..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
b0749..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
aafc2..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
87273..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
e0719..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
b0e38..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
f1358..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
f3db6..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
7c096..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
21189..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
b2758..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
aad31..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
54a2e..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
d0e7c..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
94de4..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
f630d..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
b25e2..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
9a66e..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
7cd66..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
93f0f..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
e2134..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
2dac5..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
9cd37..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
3fca5..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
4cb2c..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
ef324..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
2a1d3..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
4ee07..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
6e509..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
c4d5c..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
3a774..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
dcb32..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
50ee3..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
d3618..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
7f4ca..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
dbf71..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
08f06..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
e37fb..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
e60b6..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
78a44..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
5614a..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
af5b6..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
71ca2..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
ba478..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
be44a..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
a7e88..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
91261..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
59632..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
a8ec7..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
79ee1..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
12f92..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
f6312..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
ddb03..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
fa2d0..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
433c5..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
a1298..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
1811c..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
dd43e..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
151a9..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
4818f..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
f5518..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
4d3d7..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
3bafe..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
a1497..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
e039f..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
4086f..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
912e2..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
0d367..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
eee35..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
44916..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
b0add..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
8acce..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
86e3f..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
b47d4..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
238e3..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
74622..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
b2a43..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
0788d..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
1569d..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
5963b..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
385f8..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
fa661..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
cc30c..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
255f4..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
b44d9..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
c8a3f..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Theorem
5045a..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
0a634..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
5cc37..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
2bad0..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
33195..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
2feec..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
075bf..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
d2e51..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
e79db..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
76e3a..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
efeff..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
9eede..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
d50d0..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
ba960..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
472a0..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
74a95..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
a98e6..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
465a4..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
8ef8b..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
59a16..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
49ae6..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
94f0c..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
b1e02..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
923e2..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Known
732af..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
1b69c..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
0f029..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
∀ x4 .
x4
∈
x3
⟶
∀ x5 .
x5
∈
x3
⟶
∀ x6 .
x6
∈
x3
⟶
∀ x7 .
x7
∈
x3
⟶
∀ x8 .
x8
∈
x3
⟶
∀ x9 .
x9
∈
x3
⟶
∀ x10 .
x10
∈
x3
⟶
∀ x11 .
x11
∈
x3
⟶
∀ x12 .
x12
∈
x3
⟶
cec27..
x1
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
5bab1..
x0
x1
Theorem
9abc1..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
24cfd..
x3
x1
⟶
5bab1..
x0
x1
(proof)
Known
46936..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
889b5..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
84c45..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
71ae3..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
eb420..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
df026..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
0c026..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
6bc75..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Known
02ebd..
:
∀ x0 x1 .
∀ x2 :
ι →
ι → ο
.
(
∀ x3 .
x3
∈
x1
⟶
∀ x4 .
x4
∈
x1
⟶
x2
x3
x4
⟶
x2
x4
x3
)
⟶
4402e..
x1
x2
⟶
cf2df..
x1
x2
⟶
∀ x3 .
x3
∈
x1
⟶
x0
⊆
setminus
x1
(
Sing
x3
)
⟶
∀ x4 .
x4
∈
x0
⟶
∀ x5 .
x5
∈
x0
⟶
∀ x6 .
x6
∈
x0
⟶
∀ x7 .
x7
∈
x0
⟶
∀ x8 .
x8
∈
x0
⟶
∀ x9 .
x9
∈
x0
⟶
∀ x10 .
x10
∈
x0
⟶
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x0
⟶
43a9d..
x2
x4
x5
x6
x7
x8
x9
x10
x11
x12
⟶
∀ x13 : ο .
x13
Theorem
0d183..
:
∀ x0 .
∀ x1 :
ι →
ι → ο
.
(
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
∈
x0
⟶
x1
x2
x3
⟶
x1
x3
x2
)
⟶
4402e..
x0
x1
⟶
cf2df..
x0
x1
⟶
∀ x2 .
x2
∈
x0
⟶
∀ x3 .
x3
⊆
setminus
x0
(
Sing
x2
)
⟶
216e5..
x3
x1
⟶
∀ x4 : ο .
x4
(proof)