Let x0 of type ι be given.
Let x1 of type ι be given.
Apply mul_SNo_minus_distrL with
x0,
minus_SNo x1,
λ x2 x3 . x3 = mul_SNo x0 x1 leaving 3 subgoals.
The subproof is completed by applying H0.
Apply SNo_minus_SNo with
x1.
The subproof is completed by applying H1.
Apply mul_SNo_minus_distrR with
x0,
x1,
λ x2 x3 . minus_SNo x3 = mul_SNo x0 x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply minus_SNo_invol with
mul_SNo x0 x1.
Apply SNo_mul_SNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.