Search for blocks/addresses/...
Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Let x2 of type
ι
be given.
Assume H0:
SNo
x1
.
Assume H1:
∀ x3 .
x3
∈
SNoS_
(
SNoLev
x1
)
⟶
and
(
and
(
and
(
and
(
and
(
SNo
(
add_SNo
x0
x3
)
)
(
∀ x4 .
x4
∈
SNoL
x0
⟶
SNoLt
(
add_SNo
x4
x3
)
(
add_SNo
x0
x3
)
)
)
(
∀ x4 .
x4
∈
SNoR
x0
⟶
SNoLt
(
add_SNo
x0
x3
)
(
add_SNo
x4
x3
)
)
)
(
∀ x4 .
x4
∈
SNoL
x3
⟶
SNoLt
(
add_SNo
x0
x4
)
(
add_SNo
x0
x3
)
)
)
(
∀ x4 .
x4
∈
SNoR
x3
⟶
SNoLt
(
add_SNo
x0
x3
)
(
add_SNo
x0
x4
)
)
)
(
SNoCutP
(
binunion
{
add_SNo
x4
x3
|x4 ∈
SNoL
x0
}
(
prim5
(
SNoL
x3
)
(
add_SNo
x0
)
)
)
(
binunion
{
add_SNo
x4
x3
|x4 ∈
SNoR
x0
}
(
prim5
(
SNoR
x3
)
(
add_SNo
x0
)
)
)
)
.
Assume H2:
SNoLev
x2
∈
SNoLev
x1
.
The subproof is completed by applying H1 with
x2
.
■