Let x0 of type ι be given.
Apply ordinal_SNo with
x0.
The subproof is completed by applying H0.
Apply ordinal_SNoLev with
x0.
The subproof is completed by applying H0.
Apply set_ext with
SNoL x0,
SNoS_ x0 leaving 2 subgoals.
Let x1 of type ι be given.
Apply SNoL_E with
x0,
x1,
x1 ∈ SNoS_ x0 leaving 3 subgoals.
The subproof is completed by applying L1.
The subproof is completed by applying H3.
Apply L2 with
λ x2 x3 . x1 ∈ SNoS_ x2.
Apply SNoS_I2 with
x1,
x0 leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying L1.
The subproof is completed by applying H5.
Let x1 of type ι be given.
Assume H3:
x1 ∈ SNoS_ x0.
Apply SNoS_E2 with
x0,
x1,
x1 ∈ SNoL x0 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H3.
Apply SNoL_I with
x0,
x1 leaving 4 subgoals.
The subproof is completed by applying L1.
The subproof is completed by applying H6.
Apply L2 with
λ x2 x3 . SNoLev x1 ∈ x3.
The subproof is completed by applying H4.
Apply ordinal_SNoLev_max with
x0,
x1 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H6.
The subproof is completed by applying H4.