Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNoCutP_SNoCut with
x0,
x1,
∀ x2 . x2 ∈ x1 ⟶ SNoLt (SNoCut x0 x1) x2 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply H1 with
∀ x2 . x2 ∈ x1 ⟶ SNoLt (SNoCut x0 x1) x2.
Assume H4:
∀ x2 . x2 ∈ x1 ⟶ SNoLt (SNoCut x0 x1) x2.
The subproof is completed by applying H4.