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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: x0real.
Apply mul_i_real_eq with x0, λ x1 x2 . CSNo_Re x2 = 0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply complex_Re_eq with 0, x0 leaving 2 subgoals.
The subproof is completed by applying real_0.
The subproof is completed by applying H0.