Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNo_add_SNo with
mul_SNo (CSNo_Re x0) (CSNo_Re x1),
minus_SNo (mul_SNo (CSNo_Im x0) (CSNo_Im x1)) leaving 2 subgoals.
Apply SNo_mul_SNo with
CSNo_Re x0,
CSNo_Re x1 leaving 2 subgoals.
Apply CSNo_ReR with
x0.
The subproof is completed by applying H0.
Apply CSNo_ReR with
x1.
The subproof is completed by applying H1.
Apply SNo_minus_SNo with
mul_SNo (CSNo_Im x0) (CSNo_Im x1).
Apply SNo_mul_SNo with
CSNo_Im x0,
CSNo_Im x1 leaving 2 subgoals.
Apply CSNo_ImR with
x0.
The subproof is completed by applying H0.
Apply CSNo_ImR with
x1.
The subproof is completed by applying H1.