Let x0 of type ι be given.
Let x1 of type ι be given.
Apply mul_SNo_In_omega with
exp_SNo_nat 2 x0,
add_SNo (mul_SNo 2 x1) 1 leaving 2 subgoals.
Apply nat_p_omega with
exp_SNo_nat 2 x0.
Apply nat_exp_SNo_nat with
2,
x0 leaving 2 subgoals.
The subproof is completed by applying nat_2.
Apply omega_nat_p with
x0.
The subproof is completed by applying H0.
Apply add_SNo_In_omega with
mul_SNo 2 x1,
1 leaving 2 subgoals.
Apply mul_SNo_In_omega with
2,
x1 leaving 2 subgoals.
Apply nat_p_omega with
2.
The subproof is completed by applying nat_2.
The subproof is completed by applying H1.
Apply nat_p_omega with
1.
The subproof is completed by applying nat_1.