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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0 ∈ quaternion.
Apply quaternion_E with x0, HSNo_proj1 x0 ∈ complex leaving 2 subgoals.
The subproof is completed by applying H0.
Let x1 of type ι be given.
Assume H1: x1 ∈ complex.
Let x2 of type ι be given.
Assume H2: x2 ∈ complex.
Assume H3: x0 = CSNo_pair x1 x2.
Apply H3 with λ x3 x4 . HSNo_proj1 x4 ∈ complex.
Apply quaternion_p1_eq with x1, x2, λ x3 x4 . x4 ∈ complex leaving 3 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
The subproof is completed by applying H2.
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