Let x0 of type ι be given.
Let x1 of type ι be given.
Apply minus_SNo_invol with
x0,
λ x2 x3 . SNoLt (minus_SNo x1) x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply minus_SNo_Lt_contra with
minus_SNo x0,
x1 leaving 3 subgoals.
Apply SNo_minus_SNo with
x0.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
The subproof is completed by applying H2.