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Proofgold Term Root Disambiguation
∀ x0 x1 x2 x3 x4 x5 .
SNoCutP
x0
x1
⟶
SNoCutP
x2
x3
⟶
x4
=
SNoCut
x0
x1
⟶
x5
=
SNoCut
x2
x3
⟶
and
(
and
(
SNoCutP
(
binunion
{
add_SNo
(
mul_SNo
(
ap
x6
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x6
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x6
0
)
(
ap
x6
1
)
)
)
)
|x6 ∈
setprod
x0
x2
}
{
add_SNo
(
mul_SNo
(
ap
x6
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x6
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x6
0
)
(
ap
x6
1
)
)
)
)
|x6 ∈
setprod
x1
x3
}
)
(
binunion
{
add_SNo
(
mul_SNo
(
ap
x6
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x6
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x6
0
)
(
ap
x6
1
)
)
)
)
|x6 ∈
setprod
x0
x3
}
{
add_SNo
(
mul_SNo
(
ap
x6
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x6
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x6
0
)
(
ap
x6
1
)
)
)
)
|x6 ∈
setprod
x1
x2
}
)
)
(
mul_SNo
x4
x5
=
SNoCut
(
binunion
{
add_SNo
(
mul_SNo
(
ap
x7
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x7
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x7
0
)
(
ap
x7
1
)
)
)
)
|x7 ∈
setprod
x0
x2
}
{
add_SNo
(
mul_SNo
(
ap
x7
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x7
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x7
0
)
(
ap
x7
1
)
)
)
)
|x7 ∈
setprod
x1
x3
}
)
(
binunion
{
add_SNo
(
mul_SNo
(
ap
x7
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x7
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x7
0
)
(
ap
x7
1
)
)
)
)
|x7 ∈
setprod
x0
x3
}
{
add_SNo
(
mul_SNo
(
ap
x7
0
)
x5
)
(
add_SNo
(
mul_SNo
x4
(
ap
x7
1
)
)
(
minus_SNo
(
mul_SNo
(
ap
x7
0
)
(
ap
x7
1
)
)
)
)
|x7 ∈
setprod
x1
x2
}
)
)
)
(
∀ x6 : ο .
(
∀ x7 x8 x9 x10 .
(
∀ x11 .
x11
∈
x7
⟶
∀ x12 : ο .
(
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x2
⟶
SNo
x13
⟶
SNo
x14
⟶
SNoLt
x13
x4
⟶
SNoLt
x14
x5
⟶
x11
=
add_SNo
(
mul_SNo
x13
x5
)
(
add_SNo
(
mul_SNo
x4
x14
)
(
minus_SNo
(
mul_SNo
x13
x14
)
)
)
⟶
x12
)
⟶
x12
)
⟶
(
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x2
⟶
add_SNo
(
mul_SNo
x11
x5
)
(
add_SNo
(
mul_SNo
x4
x12
)
(
minus_SNo
(
mul_SNo
x11
x12
)
)
)
∈
x7
)
⟶
(
∀ x11 .
x11
∈
x8
⟶
∀ x12 : ο .
(
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x3
⟶
SNo
x13
⟶
SNo
x14
⟶
SNoLt
x4
x13
⟶
SNoLt
x5
x14
⟶
x11
=
add_SNo
(
mul_SNo
x13
x5
)
(
add_SNo
(
mul_SNo
x4
x14
)
(
minus_SNo
(
mul_SNo
x13
x14
)
)
)
⟶
x12
)
⟶
x12
)
⟶
(
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x3
⟶
add_SNo
(
mul_SNo
x11
x5
)
(
add_SNo
(
mul_SNo
x4
x12
)
(
minus_SNo
(
mul_SNo
x11
x12
)
)
)
∈
x8
)
⟶
(
∀ x11 .
x11
∈
x9
⟶
∀ x12 : ο .
(
∀ x13 .
x13
∈
x0
⟶
∀ x14 .
x14
∈
x3
⟶
SNo
x13
⟶
SNo
x14
⟶
SNoLt
x13
x4
⟶
SNoLt
x5
x14
⟶
x11
=
add_SNo
(
mul_SNo
x13
x5
)
(
add_SNo
(
mul_SNo
x4
x14
)
(
minus_SNo
(
mul_SNo
x13
x14
)
)
)
⟶
x12
)
⟶
x12
)
⟶
(
∀ x11 .
x11
∈
x0
⟶
∀ x12 .
x12
∈
x3
⟶
add_SNo
(
mul_SNo
x11
x5
)
(
add_SNo
(
mul_SNo
x4
x12
)
(
minus_SNo
(
mul_SNo
x11
x12
)
)
)
∈
x9
)
⟶
(
∀ x11 .
x11
∈
x10
⟶
∀ x12 : ο .
(
∀ x13 .
x13
∈
x1
⟶
∀ x14 .
x14
∈
x2
⟶
SNo
x13
⟶
SNo
x14
⟶
SNoLt
x4
x13
⟶
SNoLt
x14
x5
⟶
x11
=
add_SNo
(
mul_SNo
x13
x5
)
(
add_SNo
(
mul_SNo
x4
x14
)
(
minus_SNo
(
mul_SNo
x13
x14
)
)
)
⟶
x12
)
⟶
x12
)
⟶
(
∀ x11 .
x11
∈
x1
⟶
∀ x12 .
x12
∈
x2
⟶
add_SNo
(
mul_SNo
x11
x5
)
(
add_SNo
(
mul_SNo
x4
x12
)
(
minus_SNo
(
mul_SNo
x11
x12
)
)
)
∈
x10
)
⟶
SNoCutP
(
binunion
x7
x8
)
(
binunion
x9
x10
)
⟶
mul_SNo
x4
x5
=
SNoCut
(
binunion
x7
x8
)
(
binunion
x9
x10
)
⟶
x6
)
⟶
x6
)
as obj
-
as prop
4f23e..
mul_SNoCutP_lem
theory
HotG
stx
1941c..
address
TMGCW..
mul_SNoCutP_lem