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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
SNo
x0
.
Apply SNo_Re with
x0
,
λ x1 x2 .
minus_SNo
x0
=
SNo_pair
(
minus_SNo
x2
)
(
minus_SNo
(
CSNo_Im
x0
)
)
leaving 2 subgoals.
The subproof is completed by applying H0.
Apply SNo_Im with
x0
,
λ x1 x2 .
minus_SNo
x0
=
SNo_pair
(
minus_SNo
x0
)
(
minus_SNo
x2
)
leaving 2 subgoals.
The subproof is completed by applying H0.
Apply minus_SNo_0 with
λ x1 x2 .
minus_SNo
x0
=
SNo_pair
(
minus_SNo
x0
)
x2
.
Let x1 of type
ι
→
ι
→
ο
be given.
The subproof is completed by applying SNo_pair_0 with
minus_SNo
x0
,
λ x2 x3 .
x1
x3
x2
.
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