Let x0 of type ι be given.
Apply binunionI2 with
omega,
{minus_CSNo x1|x1 ∈ omega},
minus_SNo x0.
Apply minus_SNo_minus_CSNo with
x0,
λ x1 x2 . x2 ∈ {minus_CSNo x3|x3 ∈ omega} leaving 2 subgoals.
Apply ordinal_SNo with
x0.
Apply nat_p_ordinal with
x0.
Apply omega_nat_p with
x0.
The subproof is completed by applying H0.
Apply ReplI with
omega,
minus_CSNo,
x0.
The subproof is completed by applying H0.