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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
CSNo
x0
.
Apply Re_0 with
λ x1 x2 .
SNo_pair
(
add_SNo
(
CSNo_Re
x0
)
x2
)
(
add_SNo
(
CSNo_Im
x0
)
(
CSNo_Im
0
)
)
=
x0
.
Apply Im_0 with
λ x1 x2 .
SNo_pair
(
add_SNo
(
CSNo_Re
x0
)
0
)
(
add_SNo
(
CSNo_Im
x0
)
x2
)
=
x0
.
Apply add_SNo_0R with
CSNo_Re
x0
,
λ x1 x2 .
SNo_pair
x2
(
add_SNo
(
CSNo_Im
x0
)
0
)
=
x0
leaving 2 subgoals.
Apply CSNo_ReR with
x0
.
The subproof is completed by applying H0.
Apply add_SNo_0R with
CSNo_Im
x0
,
λ x1 x2 .
SNo_pair
(
CSNo_Re
x0
)
x2
=
x0
leaving 2 subgoals.
Apply CSNo_ImR with
x0
.
The subproof is completed by applying H0.
Let x1 of type
ι
→
ι
→
ο
be given.
Apply CSNo_ReIm with
x0
,
λ x2 x3 .
x1
x3
x2
.
The subproof is completed by applying H0.
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