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Proofgold Proof
pf
Let x0 of type
ι
be given.
Let x1 of type
ι
be given.
Assume H0:
SNoCutP
x0
x1
.
Assume H1:
∀ x2 .
x2
∈
x0
⟶
minus_SNo
(
minus_SNo
x2
)
=
x2
.
Assume H2:
∀ x2 .
x2
∈
x0
⟶
SNo
x2
.
Assume H3:
∀ x2 .
x2
∈
x1
⟶
SNo
x2
.
Assume H4:
SNo
(
SNoCut
x0
x1
)
.
Apply minus_SNo_invol with
SNoCut
x0
x1
.
The subproof is completed by applying H4.
■