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Proofgold Proposition
∀ x0 x1 .
∀ x2 x3 :
ι →
ι → ι
.
SNo
x0
⟶
SNo
x1
⟶
(
∀ x4 .
x4
∈
SNoS_
(
SNoLev
x0
)
⟶
∀ x5 .
SNo
x5
⟶
x2
x4
x5
=
x3
x4
x5
)
⟶
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoL
x1
)
}
=
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoL
x1
)
}
⟶
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoR
x1
)
}
=
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoR
x1
)
}
⟶
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoR
x1
)
}
=
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoR
x1
)
}
⟶
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoL
x1
)
}
=
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoL
x1
)
}
⟶
SNoCut
(
binunion
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoL
x1
)
}
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoR
x1
)
}
)
(
binunion
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoR
x1
)
}
{
add_SNo
(
x2
(
ap
x5
0
)
x1
)
(
add_SNo
(
x2
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x2
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoL
x1
)
}
)
=
SNoCut
(
binunion
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoL
x1
)
}
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoR
x1
)
}
)
(
binunion
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoL
x0
)
(
SNoR
x1
)
}
{
add_SNo
(
x3
(
ap
x5
0
)
x1
)
(
add_SNo
(
x3
x0
(
ap
x5
1
)
)
(
minus_SNo
(
x3
(
ap
x5
0
)
(
ap
x5
1
)
)
)
)
|x5 ∈
setprod
(
SNoR
x0
)
(
SNoL
x1
)
}
)
type
prop
theory
HotG
name
-
proof
PURzn..
Megalodon
Conj_mul_SNo_eq__25__3
proofgold address
TMPpy..
Conj_mul_SNo_eq__25__3
creator
35045
PrNpY..
/
edbb1..
owner
35047
PrNpY..
/
d3773..
term root
aae1c..