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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 ιιο be given.
Apply CSNo_ReIm with x0, λ x2 x3 . x1 x3 x2.
The subproof is completed by applying H0.