Let x0 of type ι → ο be given.
Assume H0:
∀ x1 . x1 ∈ omega ⟶ x0 x1.
Apply int_SNo_cases with
x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Let x1 of type ι be given.
Apply minus_SNo_minus_CSNo with
x1,
λ x2 x3 . x0 x3 leaving 2 subgoals.
Apply omega_SNo with
x1.
The subproof is completed by applying H2.
Apply H1 with
x1.
The subproof is completed by applying H2.