Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNo_SNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply SNoLev_uniq2 with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply minus_SNo_Lev with
x1,
λ x2 x3 . x3 = x0 leaving 2 subgoals.
The subproof is completed by applying L2.
The subproof is completed by applying L3.
Apply L4 with
λ x2 x3 . SNo_ x2 (minus_SNo x1).
Apply SNoLev_ with
minus_SNo x1.
Apply SNo_minus_SNo with
x1.
The subproof is completed by applying L2.