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Proofgold Proof
pf
Apply HSNo_proj0proj1_split with
conj_HSNo
Quaternion_k
,
minus_HSNo
Quaternion_k
leaving 4 subgoals.
Apply HSNo_conj_HSNo with
Quaternion_k
.
The subproof is completed by applying HSNo_Quaternion_k.
Apply HSNo_minus_HSNo with
Quaternion_k
.
The subproof is completed by applying HSNo_Quaternion_k.
Apply conj_HSNo_proj0 with
Quaternion_k
,
λ x0 x1 .
x1
=
HSNo_proj0
(
minus_HSNo
Quaternion_k
)
leaving 2 subgoals.
The subproof is completed by applying HSNo_Quaternion_k.
Apply minus_HSNo_proj0 with
Quaternion_k
,
λ x0 x1 .
conj_CSNo
(
HSNo_proj0
Quaternion_k
)
=
x1
leaving 2 subgoals.
The subproof is completed by applying HSNo_Quaternion_k.
Apply HSNo_p0_k with
λ x0 x1 .
conj_CSNo
x1
=
minus_CSNo
x1
.
Apply minus_CSNo_0 with
λ x0 x1 .
conj_CSNo
0
=
x1
.
Apply conj_CSNo_id_SNo with
0
.
The subproof is completed by applying SNo_0.
Apply conj_HSNo_proj1 with
Quaternion_k
,
λ x0 x1 .
x1
=
HSNo_proj1
(
minus_HSNo
Quaternion_k
)
leaving 2 subgoals.
The subproof is completed by applying HSNo_Quaternion_k.
Apply minus_HSNo_proj1 with
Quaternion_k
,
λ x0 x1 .
minus_CSNo
(
HSNo_proj1
Quaternion_k
)
=
x1
leaving 2 subgoals.
The subproof is completed by applying HSNo_Quaternion_k.
Let x0 of type
ι
→
ι
→
ο
be given.
Assume H0:
x0
(
minus_CSNo
(
HSNo_proj1
Quaternion_k
)
)
(
minus_CSNo
(
HSNo_proj1
Quaternion_k
)
)
.
The subproof is completed by applying H0.
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