Let x0 of type ι be given.
Apply xm with
SNoLe 0 x0,
SNo (abs_SNo x0) leaving 2 subgoals.
Apply nonneg_abs_SNo with
x0,
λ x1 x2 . SNo x2 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply not_nonneg_abs_SNo with
x0,
λ x1 x2 . SNo x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply SNo_minus_SNo with
x0.
The subproof is completed by applying H0.