Let x0 of type ι be given.
Apply and3I with
1 ∈ int,
x0 ∈ int,
∃ x1 . and (x1 ∈ int) (mul_SNo 1 x1 = x0) leaving 3 subgoals.
Apply Subq_omega_int with
1.
Apply nat_p_omega with
1.
The subproof is completed by applying nat_1.
The subproof is completed by applying H0.
Let x1 of type ο be given.
Apply H1 with
x0.
Apply andI with
x0 ∈ int,
mul_SNo 1 x0 = x0 leaving 2 subgoals.
The subproof is completed by applying H0.
Apply mul_SNo_oneL with
x0.
Apply int_SNo with
x0.
The subproof is completed by applying H0.