Let x0 of type ι be given.
Let x1 of type ι be given.
Apply and3I with
x0 ∈ omega,
mul_SNo x0 x1 ∈ omega,
∃ x2 . and (x2 ∈ omega) (mul_nat x0 x2 = mul_SNo x0 x1) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply mul_SNo_In_omega with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
Let x2 of type ο be given.
Apply H2 with
x1.
Apply andI with
x1 ∈ omega,
mul_nat x0 x1 = mul_SNo x0 x1 leaving 2 subgoals.
The subproof is completed by applying H1.
Apply mul_nat_mul_SNo with
x0,
x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.