Let x0 of type ι be given.
Let x1 of type ι be given.
Let x2 of type ι be given.
Apply minus_SNo_invol with
x0,
λ x3 x4 . SNoLe (add_SNo x2 (minus_SNo x1)) x3 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply minus_SNo_Le_swap with
minus_SNo x0,
x1,
x2 leaving 4 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.
The subproof is completed by applying H3.