Let x0 of type ι be given.
Apply and3I with
x0 ∈ int,
0 ∈ int,
∃ x1 . and (x1 ∈ int) (mul_SNo x0 x1 = 0) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply nat_p_int with
0.
The subproof is completed by applying nat_0.
Let x1 of type ο be given.
Apply H1 with
0.
Apply andI with
0 ∈ int,
mul_SNo x0 0 = 0 leaving 2 subgoals.
Apply nat_p_int with
0.
The subproof is completed by applying nat_0.
Apply mul_SNo_zeroR with
x0.
Apply int_SNo with
x0.
The subproof is completed by applying H0.