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Proofgold Proof
pf
Let x0 of type
ι
be given.
Assume H0:
x0
∈
complex
.
Let x1 of type
ι
be given.
Assume H1:
x1
∈
complex
.
Apply tuple_2_0_eq with
x0
,
x1
,
λ x2 x3 .
CSNo_pair
x2
x1
∈
quaternion
.
Apply tuple_2_1_eq with
x0
,
x1
,
λ x2 x3 .
CSNo_pair
(
ap
(
lam
2
(
λ x4 .
If_i
(
x4
=
0
)
x0
x1
)
)
0
)
x2
∈
quaternion
.
Apply ReplI with
setprod
complex
complex
,
λ x2 .
CSNo_pair
(
ap
x2
0
)
(
ap
x2
1
)
,
lam
2
(
λ x2 .
If_i
(
x2
=
0
)
x0
x1
)
.
Apply tuple_2_setprod with
complex
,
complex
,
x0
,
x1
leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
■