Let x0 of type ι be given.
Let x1 of type ι be given.
Apply set_ext with
x0,
x1 leaving 2 subgoals.
Apply SNo_Subq with
x0,
x1 leaving 4 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply H2 with
λ x2 x3 . SNoLev x0 ⊆ x2.
The subproof is completed by applying Subq_ref with
SNoLev x0.
The subproof is completed by applying H3.
Apply SNo_Subq with
x1,
x0 leaving 4 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.
Apply H2 with
λ x2 x3 . SNoLev x1 ⊆ x3.
The subproof is completed by applying Subq_ref with
SNoLev x1.
Let x2 of type ι be given.
Apply iff_sym with
x2 ∈ x0,
x2 ∈ x1.
Apply H3 with
x2.
Apply H2 with
λ x3 x4 . x2 ∈ x4.
The subproof is completed by applying H4.