Let x0 of type ι be given.
Apply mul_nat_SR with
x0,
0,
λ x1 x2 . x2 = x0 leaving 2 subgoals.
The subproof is completed by applying nat_0.
Apply mul_nat_0R with
x0,
λ x1 x2 . add_nat x0 x2 = x0.
The subproof is completed by applying add_nat_0R with x0.