Let x0 of type ι be given.
Apply ordinal_ordsucc_SNo_eq with
x0,
λ x1 x2 . add_SNo (minus_SNo 1) x2 = x0 leaving 2 subgoals.
Apply nat_p_ordinal with
x0.
The subproof is completed by applying H0.
Apply add_SNo_minus_L2 with
1,
x0 leaving 2 subgoals.
The subproof is completed by applying SNo_1.
Apply nat_p_SNo with
x0.
The subproof is completed by applying H0.