Let x0 of type ι be given.
Apply SNo_minus_SNo with
x0.
The subproof is completed by applying H0.
Apply add_SNo_com with
x0,
minus_SNo x0,
λ x1 x2 . x2 = 0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L1.
Apply add_SNo_minus_SNo_linv with
x0.
The subproof is completed by applying H0.