Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNo_minus_SNo with
x1.
The subproof is completed by applying H1.
Apply minus_SNo_Lev with
x1,
λ x2 x3 . x3 ∈ ordsucc x0 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H2.
Apply minus_SNo_invol with
x1,
λ x2 x3 . SNoLe (minus_SNo x0) x2 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply minus_SNo_Le_contra with
minus_SNo x1,
x0 leaving 3 subgoals.
The subproof is completed by applying L3.
Apply ordinal_SNo with
x0.
The subproof is completed by applying H0.
Apply ordinal_SNoLev_max_2 with
x0,
minus_SNo x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying L3.
The subproof is completed by applying L4.