Let x0 of type ι be given.
Let x1 of type ι be given.
Apply SNoS_E2 with
omega,
x0,
add_CSNo x0 x1 ∈ SNoS_ omega leaving 3 subgoals.
The subproof is completed by applying omega_ordinal.
The subproof is completed by applying H0.
Apply SNoS_E2 with
omega,
x1,
add_CSNo x0 x1 ∈ SNoS_ omega leaving 3 subgoals.
The subproof is completed by applying omega_ordinal.
The subproof is completed by applying H1.
Apply add_SNo_add_CSNo with
x0,
x1,
λ x2 x3 . x2 ∈ SNoS_ omega leaving 3 subgoals.
The subproof is completed by applying H4.
The subproof is completed by applying H8.
Apply add_SNo_SNoS_omega with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.