Let x0 of type ι be given.
Let x1 of type ι be given.
Apply add_nat_add_SNo with
x0,
ordsucc x1,
λ x2 x3 . x2 = ordsucc (add_SNo x0 x1) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply omega_ordsucc with
x1.
The subproof is completed by applying H1.
Apply add_nat_add_SNo with
x0,
x1,
λ x2 x3 . add_nat x0 (ordsucc x1) = ordsucc x2 leaving 3 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Apply add_nat_SR with
x0,
x1.
Apply omega_nat_p with
x1.
The subproof is completed by applying H1.