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Proofgold Proposition
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 :
ι →
ι → ι
.
62ee1..
x0
x1
x2
x3
x4
x5
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
x6
x7
x8
=
x6
x9
x10
⟶
and
(
x7
=
x9
)
(
x8
=
x10
)
)
⟶
explicit_Field
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
λ x7 x8 .
x6
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
)
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
)
)
(
λ x7 x8 .
x6
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
)
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
)
)
)
⟶
and
(
11fac..
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
∀ x9 : ο .
(
∀ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
x8
x10
)
⟶
x9
)
⟶
x9
)
)
)
x1
)
(
λ x7 .
x6
(
prim0
(
λ x8 .
and
(
prim1
x8
x0
)
(
x7
=
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
x8
)
)
)
x1
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
x6
x1
x2
)
(
λ x7 x8 .
x6
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
)
(
x3
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
)
)
(
λ x7 x8 .
x6
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x8
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
)
(
x4
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
x7
=
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x7
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x9
)
)
)
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
)
)
)
)
(
(
∀ x7 .
prim1
x7
x0
⟶
x6
x7
x1
=
x7
)
⟶
and
(
and
(
and
(
and
(
and
(
Subq
x0
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
)
(
∀ x7 .
prim1
x7
x0
⟶
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
=
x7
)
)
(
x6
x1
x1
=
x1
)
)
(
x6
x2
x1
=
x2
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
=
x3
x7
x8
)
)
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x7
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x8
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x8
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x7
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x7
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
)
=
x4
x7
x8
)
)
type
prop
theory
HoTg
name
-
proof
PULBv..
Megalodon
-
proofgold address
TMTRU..
creator
3879
PrGxv..
/
df55f..
owner
3879
PrGxv..
/
df55f..
term root
c7fbc..