Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNoCutP_SNoCut with
x0,
x1,
∀ x2 . SNo x2 ⟶ (∀ x3 . x3 ∈ x0 ⟶ SNoLt x3 x2) ⟶ (∀ x3 . x3 ∈ x1 ⟶ SNoLt x2 x3) ⟶ and (SNoLev (SNoCut x0 x1) ⊆ SNoLev x2) (SNoEq_ (SNoLev (SNoCut x0 x1)) (SNoCut x0 x1) x2) leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H2.