Let x0 of type ι be given.
Apply SNoLtI2 with
x0,
SNo_extend1 x0 leaving 3 subgoals.
Apply SNo_extend1_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 SNoEq_sym_ with
SNoLev x0,
SNo_extend1 x0,
x0.
Apply SNo_extend1_SNoEq with
x0.
The subproof is completed by applying H0.
Apply SNo_extend1_In with
x0.
The subproof is completed by applying H0.