Let x0 of type ι be given.
Apply SNoLtI3 with
SNo_extend0 x0,
x0 leaving 3 subgoals.
Apply SNo_extend0_SNoLev with
x0,
λ x1 x2 . SNoLev x0 ∈ x2 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying ordsuccI2 with
SNoLev x0.
Apply SNo_extend0_SNoEq with
x0.
The subproof is completed by applying H0.
Apply SNo_extend0_nIn with
x0.
The subproof is completed by applying H0.