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Proofgold Asset
asset id
be09426d48dbf67d2665be068d41bc68071fa8475187459bec6fe9cadc26bfa7
asset hash
75b0d48d2b9340b66ed8256699378e838098d8c024481eefcda82b9915f0a688
bday / block
3879
tx
d79c1..
preasset
doc published by
PrGxv..
Param
explicit_Field
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
ο
Param
explicit_Field_minus
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
ι
→
ι
Known
2f9e6..
:
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
explicit_Field
x0
x1
x2
x3
x4
⟶
∀ x5 : ο .
(
(
∀ x6 .
prim1
x6
x0
⟶
prim1
(
explicit_Field_minus
x0
x1
x2
x3
x4
x6
)
x0
)
⟶
explicit_Field_minus
x0
x1
x2
x3
x4
x1
=
x1
⟶
(
∀ x6 .
prim1
x6
x0
⟶
explicit_Field_minus
x0
x1
x2
x3
x4
(
explicit_Field_minus
x0
x1
x2
x3
x4
x6
)
=
x6
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
x3
(
explicit_Field_minus
x0
x1
x2
x3
x4
x6
)
x6
=
x1
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
x3
x6
(
explicit_Field_minus
x0
x1
x2
x3
x4
x6
)
=
x1
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x4
(
x3
x6
x7
)
x8
=
x3
(
x4
x6
x8
)
(
x4
x7
x8
)
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
explicit_Field_minus
x0
x1
x2
x3
x4
(
x3
x6
x7
)
=
x3
(
explicit_Field_minus
x0
x1
x2
x3
x4
x6
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
x7
)
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
x4
(
explicit_Field_minus
x0
x1
x2
x3
x4
x6
)
x7
=
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
x6
x7
)
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
x4
x6
(
explicit_Field_minus
x0
x1
x2
x3
x4
x7
)
=
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
x6
x7
)
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
x4
x1
x6
=
x1
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
x4
x6
x1
=
x1
)
⟶
prim1
(
explicit_Field_minus
x0
x1
x2
x3
x4
x2
)
x0
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
prim1
(
x4
x6
(
x4
x7
x8
)
)
x0
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x3
(
x3
x6
x7
)
(
x3
x8
x9
)
=
x3
(
x3
x6
x9
)
(
x3
x7
x8
)
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x3
(
x3
x6
x7
)
(
x3
x8
x9
)
=
x3
(
x3
x6
x8
)
(
x3
x7
x9
)
)
⟶
x5
)
⟶
x5
Param
62ee1..
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ο
) →
ο
Param
and
:
ο
→
ο
→
ο
Param
3b429..
:
ι
→
(
ι
→
ι
) →
(
ι
→
ι
→
ο
) →
CT2
ι
Param
True
:
ο
Param
1216a..
:
ι
→
(
ι
→
ο
) →
ι
Known
6e27d..
:
∀ 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
)
)
⟶
∀ x7 : ο .
(
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim1
(
x6
x8
x9
)
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 :
ι → ο
.
(
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x8
=
x6
x10
x11
⟶
x9
(
x6
x10
x11
)
)
⟶
x9
x8
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
=
x8
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
=
x9
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
prim1
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
x0
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
prim1
(
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
)
)
)
x0
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
x8
=
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
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
)
)
)
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
prim1
(
x6
x8
x1
)
(
1216a..
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
(
λ x9 .
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x1
=
x9
)
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
=
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
=
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
⟶
x8
=
x9
)
⟶
prim1
(
x6
x1
x1
)
(
3b429..
x0
(
λ x8 .
x0
)
(
λ x8 x9 .
True
)
x6
)
⟶
prim1
(
x6
x2
x1
)
(
3b429..
x0
(
λ x8 .
x0
)
(
λ x8 x9 .
True
)
x6
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
=
x6
(
x3
x8
x10
)
(
x3
x9
x11
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
x6
(
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
(
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
=
x6
(
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
(
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim1
(
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
x3
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
)
(
x3
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
x15
)
)
)
)
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
=
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
(
x3
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
)
(
x3
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∀ x20 : ο .
(
∀ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
⟶
x20
)
⟶
x20
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∀ x20 : ο .
(
∀ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
⟶
x20
)
⟶
x20
)
)
)
x17
)
)
)
)
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
=
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
)
=
x6
(
x3
(
x4
x8
x10
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
x9
x11
)
)
)
(
x3
(
x4
x8
x11
)
(
x4
x9
x10
)
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
x6
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
)
=
x6
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim1
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
)
x0
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim1
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
)
x0
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim1
(
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
)
)
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
x15
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
x15
)
)
)
)
(
x4
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
x15
)
)
)
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
)
)
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
=
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
)
)
⟶
(
∀ x8 .
prim1
x8
(
3b429..
x0
(
λ x9 .
x0
)
(
λ x9 x10 .
True
)
x6
)
⟶
∀ x9 .
prim1
x9
(
3b429..
x0
(
λ x10 .
x0
)
(
λ x10 x11 .
True
)
x6
)
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
)
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∀ x20 : ο .
(
∀ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
⟶
x20
)
⟶
x20
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∀ x20 : ο .
(
∀ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
⟶
x20
)
⟶
x20
)
)
)
x17
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x8
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x9
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∀ x20 : ο .
(
∀ x21 .
and
(
prim1
x21
x0
)
(
x9
=
x6
x19
x21
)
⟶
x20
)
⟶
x20
)
)
)
x17
)
)
)
)
(
x4
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
x8
=
x6
(
prim0
(
λ x19 .
and
(
prim1
x19
x0
)
(
∀ x20 : ο .
(
∀ x21 .
and
(
prim1
x21
x0
)
(
x8
=
x6
x19
x21
)
⟶
x20
)
⟶
x20
)
)
)
x17
)
)
)
(
prim0
(
λ x17 .
and
(
prim1
x17
x0
)
(
∀ x18 : ο .
(
∀ x19 .
and
(
prim1
x19
x0
)
(
x9
=
x6
x17
x19
)
⟶
x18
)
⟶
x18
)
)
)
)
)
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
=
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
)
⟶
x7
)
⟶
x7
Known
b6a82..
:
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
x8
x9
=
x6
x10
x11
⟶
and
(
x8
=
x10
)
(
x9
=
x11
)
)
⟶
62ee1..
x0
x1
x2
x3
x4
x5
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x3
x8
x9
=
x3
x9
x8
)
⟶
prim1
x1
x0
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x3
x1
x8
=
x8
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim1
(
x4
x8
x9
)
x0
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
=
x8
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
prim1
(
x6
x8
x1
)
(
1216a..
x7
(
λ x9 .
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x1
=
x9
)
)
)
⟶
(
∀ x8 .
prim1
x8
x7
⟶
prim1
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
x0
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
=
x6
(
x3
x8
x10
)
(
x3
x9
x11
)
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
)
=
x6
(
x3
(
x4
x8
x10
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
x9
x11
)
)
)
(
x3
(
x4
x8
x11
)
(
x4
x9
x10
)
)
)
⟶
explicit_Field_minus
x0
x1
x2
x3
x4
x1
=
x1
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x4
x1
x8
=
x1
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x4
x8
x1
=
x1
)
⟶
62ee1..
(
1216a..
x7
(
λ x8 .
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
x1
=
x8
)
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
λ x8 x9 .
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
x3
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
(
λ x8 x9 .
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
)
)
(
λ x8 x9 .
x5
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
Param
11fac..
:
ι
→
(
ι
→
ι
) →
(
ι
→
ι
) →
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
ο
Param
Subq
:
ι
→
ι
→
ο
Known
65b0c..
:
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 :
ι →
ι → ι
.
∀ x7 .
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
x8
x9
=
x6
x10
x11
⟶
and
(
x8
=
x10
)
(
x9
=
x11
)
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim1
(
x3
x8
x9
)
x0
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x3
x8
x9
=
x3
x9
x8
)
⟶
prim1
x1
x0
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x3
x1
x8
=
x8
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim1
(
x4
x8
x9
)
x0
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x4
x8
x9
=
x4
x9
x8
)
⟶
prim1
x2
x0
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x4
x2
x8
=
x8
)
⟶
prim1
(
explicit_Field_minus
x0
x1
x2
x3
x4
x2
)
x0
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim1
(
x6
x8
x9
)
x7
)
⟶
(
∀ x8 .
prim1
x8
x7
⟶
∀ x9 :
ι → ο
.
(
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x8
=
x6
x10
x11
⟶
x9
(
x6
x10
x11
)
)
⟶
x9
x8
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
=
x8
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
=
x9
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
prim1
(
x6
x8
x1
)
(
1216a..
x7
(
λ x9 .
x6
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
x1
=
x9
)
)
)
⟶
(
∀ x8 .
prim1
x8
x7
⟶
prim1
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
x0
)
⟶
(
∀ x8 .
prim1
x8
x7
⟶
prim1
(
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
)
)
)
x0
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
x3
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
=
x6
(
x3
x8
x10
)
(
x3
x9
x11
)
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
∀ x10 .
prim1
x10
x0
⟶
∀ x11 .
prim1
x11
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x8
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x10
x11
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x10
x11
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
)
(
x4
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
x6
x8
x9
=
x6
(
prim0
(
λ x15 .
and
(
prim1
x15
x0
)
(
∀ x16 : ο .
(
∀ x17 .
and
(
prim1
x17
x0
)
(
x6
x8
x9
=
x6
x15
x17
)
⟶
x16
)
⟶
x16
)
)
)
x13
)
)
)
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x6
x10
x11
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
)
)
=
x6
(
x3
(
x4
x8
x10
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
x9
x11
)
)
)
(
x3
(
x4
x8
x11
)
(
x4
x9
x10
)
)
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x3
(
explicit_Field_minus
x0
x1
x2
x3
x4
x8
)
x8
=
x1
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x3
x8
(
explicit_Field_minus
x0
x1
x2
x3
x4
x8
)
=
x1
)
⟶
explicit_Field_minus
x0
x1
x2
x3
x4
x1
=
x1
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x4
x1
x8
=
x1
)
⟶
(
∀ x8 .
prim1
x8
x0
⟶
x4
x8
x1
=
x1
)
⟶
explicit_Field
x7
(
x6
x1
x1
)
(
x6
x2
x1
)
(
λ x8 x9 .
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
x3
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
(
λ x8 x9 .
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
)
)
⟶
62ee1..
(
1216a..
x7
(
λ x8 .
x6
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
x1
=
x8
)
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
λ x8 x9 .
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
x3
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
(
λ x8 x9 .
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
)
)
(
λ x8 x9 .
x5
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
⟶
and
(
11fac..
x7
(
λ x8 .
x6
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
x1
)
(
λ x8 .
x6
(
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
)
)
)
x1
)
(
x6
x1
x1
)
(
x6
x2
x1
)
(
x6
x1
x2
)
(
λ x8 x9 .
x6
(
x3
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
x3
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
(
λ x8 x9 .
x6
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
x9
=
x6
(
prim0
(
λ x12 .
and
(
prim1
x12
x0
)
(
∀ x13 : ο .
(
∀ x14 .
and
(
prim1
x14
x0
)
(
x9
=
x6
x12
x14
)
⟶
x13
)
⟶
x13
)
)
)
x10
)
)
)
)
(
x4
(
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
)
)
)
(
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x9
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
)
)
)
)
)
(
(
∀ x8 .
prim1
x8
x0
⟶
x6
x8
x1
=
x8
)
⟶
and
(
and
(
and
(
and
(
and
(
Subq
x0
x7
)
(
∀ x8 .
prim1
x8
x0
⟶
prim0
(
λ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 : ο .
(
∀ x12 .
and
(
prim1
x12
x0
)
(
x8
=
x6
x10
x12
)
⟶
x11
)
⟶
x11
)
)
=
x8
)
)
(
x6
x1
x1
=
x1
)
)
(
x6
x2
x1
=
x2
)
)
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x6
(
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
(
x3
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
=
x3
x8
x9
)
)
(
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x6
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
(
explicit_Field_minus
x0
x1
x2
x3
x4
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
)
)
(
x3
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x8
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x9
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x9
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
)
(
x4
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
x8
=
x6
(
prim0
(
λ x13 .
and
(
prim1
x13
x0
)
(
∀ x14 : ο .
(
∀ x15 .
and
(
prim1
x15
x0
)
(
x8
=
x6
x13
x15
)
⟶
x14
)
⟶
x14
)
)
)
x11
)
)
)
(
prim0
(
λ x11 .
and
(
prim1
x11
x0
)
(
∀ x12 : ο .
(
∀ x13 .
and
(
prim1
x13
x0
)
(
x9
=
x6
x11
x13
)
⟶
x12
)
⟶
x12
)
)
)
)
)
=
x4
x8
x9
)
)
Param
explicit_OrderedField
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ο
) →
ο
Param
lt
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ο
) →
ι
→
ι
→
ο
Param
natOfOrderedField_p
:
ι
→
ι
→
ι
→
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ι
) →
(
ι
→
ι
→
ο
) →
ι
→
ο
Param
b5c9f..
:
ι
→
ι
→
ι
Param
f482f..
:
ι
→
ι
→
ι
Known
f2fa8..
:
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 : ο .
(
62ee1..
x0
x1
x2
x3
x4
x5
⟶
explicit_OrderedField
x0
x1
x2
x3
x4
x5
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
lt
x0
x1
x2
x3
x4
x5
x1
x7
⟶
x5
x1
x8
⟶
∀ x9 : ο .
(
∀ x10 .
and
(
prim1
x10
(
1216a..
x0
(
natOfOrderedField_p
x0
x1
x2
x3
x4
x5
)
)
)
(
x5
x8
(
x4
x10
x7
)
)
⟶
x9
)
⟶
x9
)
⟶
(
∀ x7 .
prim1
x7
(
b5c9f..
x0
(
1216a..
x0
(
natOfOrderedField_p
x0
x1
x2
x3
x4
x5
)
)
)
⟶
∀ x8 .
prim1
x8
(
b5c9f..
x0
(
1216a..
x0
(
natOfOrderedField_p
x0
x1
x2
x3
x4
x5
)
)
)
⟶
(
∀ x9 .
prim1
x9
(
1216a..
x0
(
natOfOrderedField_p
x0
x1
x2
x3
x4
x5
)
)
⟶
and
(
and
(
x5
(
f482f..
x7
x9
)
(
f482f..
x8
x9
)
)
(
x5
(
f482f..
x7
x9
)
(
f482f..
x7
(
x3
x9
x2
)
)
)
)
(
x5
(
f482f..
x8
(
x3
x9
x2
)
)
(
f482f..
x8
x9
)
)
)
⟶
∀ x9 : ο .
(
∀ x10 .
and
(
prim1
x10
x0
)
(
∀ x11 .
prim1
x11
(
1216a..
x0
(
natOfOrderedField_p
x0
x1
x2
x3
x4
x5
)
)
⟶
and
(
x5
(
f482f..
x7
x11
)
x10
)
(
x5
x10
(
f482f..
x8
x11
)
)
)
⟶
x9
)
⟶
x9
)
⟶
x6
)
⟶
62ee1..
x0
x1
x2
x3
x4
x5
⟶
x6
Param
iff
:
ο
→
ο
→
ο
Param
or
:
ο
→
ο
→
ο
Known
explicit_OrderedField_E
:
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 :
ι →
ι → ο
.
∀ x6 : ο .
(
explicit_OrderedField
x0
x1
x2
x3
x4
x5
⟶
explicit_Field
x0
x1
x2
x3
x4
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x5
x7
x8
⟶
x5
x8
x9
⟶
x5
x7
x9
)
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
iff
(
and
(
x5
x7
x8
)
(
x5
x8
x7
)
)
(
x7
=
x8
)
)
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
or
(
x5
x7
x8
)
(
x5
x8
x7
)
)
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
∀ x9 .
prim1
x9
x0
⟶
x5
x7
x8
⟶
x5
(
x3
x7
x9
)
(
x3
x8
x9
)
)
⟶
(
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x5
x1
x7
⟶
x5
x1
x8
⟶
x5
x1
(
x4
x7
x8
)
)
⟶
x6
)
⟶
explicit_OrderedField
x0
x1
x2
x3
x4
x5
⟶
x6
Known
explicit_Field_E
:
∀ x0 x1 x2 .
∀ x3 x4 :
ι →
ι → ι
.
∀ x5 : ο .
(
explicit_Field
x0
x1
x2
x3
x4
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
prim1
(
x3
x6
x7
)
x0
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x3
x6
(
x3
x7
x8
)
=
x3
(
x3
x6
x7
)
x8
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
x3
x6
x7
=
x3
x7
x6
)
⟶
prim1
x1
x0
⟶
(
∀ x6 .
prim1
x6
x0
⟶
x3
x1
x6
=
x6
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 : ο .
(
∀ x8 .
and
(
prim1
x8
x0
)
(
x3
x6
x8
=
x1
)
⟶
x7
)
⟶
x7
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
prim1
(
x4
x6
x7
)
x0
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x4
x6
(
x4
x7
x8
)
=
x4
(
x4
x6
x7
)
x8
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
x4
x6
x7
=
x4
x7
x6
)
⟶
prim1
x2
x0
⟶
(
x2
=
x1
⟶
∀ x6 : ο .
x6
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
x4
x2
x6
=
x6
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
(
x6
=
x1
⟶
∀ x7 : ο .
x7
)
⟶
∀ x7 : ο .
(
∀ x8 .
and
(
prim1
x8
x0
)
(
x4
x6
x8
=
x2
)
⟶
x7
)
⟶
x7
)
⟶
(
∀ x6 .
prim1
x6
x0
⟶
∀ x7 .
prim1
x7
x0
⟶
∀ x8 .
prim1
x8
x0
⟶
x4
x6
(
x3
x7
x8
)
=
x3
(
x4
x6
x7
)
(
x4
x6
x8
)
)
⟶
x5
)
⟶
explicit_Field
x0
x1
x2
x3
x4
⟶
x5
Theorem
b4fdd..
:
∀ 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
)
)
⟶
62ee1..
(
1216a..
(
3b429..
x0
(
λ x7 .
x0
)
(
λ x7 x8 .
True
)
x6
)
(
λ x7 .
x6
(
prim0
(
λ x9 .
and
(
prim1
x9
x0
)
(
∀ x10 : ο .
(
∀ x11 .
and
(
prim1
x11
x0
)
(
x7
=
x6
x9
x11
)
⟶
x10
)
⟶
x10
)
)
)
x1
=
x7
)
)
(
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
)
)
)
)
)
)
(
λ x7 x8 .
x5
(
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
)
)
)
)
(proof)
Theorem
424a2..
:
∀ 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
)
)
(proof)