Let x0 of type ι be given.
Let x1 of type ι be given.
Apply minus_SNo_invol with
x1,
λ x2 x3 . add_SNo (add_SNo x0 (minus_SNo x1)) x2 = x0 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply add_SNo_minus_R2 with
x0,
minus_SNo x1 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply SNo_minus_SNo with
x1.
The subproof is completed by applying H1.