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 Empty_Subq_eq with
SNoR x0.
Let x1 of type ι be given.
Apply SNoR_E with
x0,
x1,
x1 ∈ 0 leaving 3 subgoals.
The subproof is completed by applying L1.
The subproof is completed by applying H3.
Apply L2 with
λ x2 x3 . SNoLev x1 ∈ x3 ⟶ SNoLt x0 x1 ⟶ x1 ∈ 0.
Apply FalseE with
x1 ∈ 0.
Apply SNoLt_irref with
x1.
Apply SNoLt_tra with
x1,
x0,
x1 leaving 5 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying L1.
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 H4.
The subproof is completed by applying H5.
The subproof is completed by applying H6.