Let x0 of type ι be given.
Apply mul_nat_mul_SNo with
2,
x0,
λ x1 x2 . even_nat x1 leaving 3 subgoals.
Apply nat_p_omega with
2.
The subproof is completed by applying nat_2.
The subproof is completed by applying H0.
Apply even_nat_double with
x0.
Apply omega_nat_p with
x0.
The subproof is completed by applying H0.