Let x0 of type ι be given.
Apply nat_primrec_S with
1,
λ x1 x2 . mul_nat x0 x2,
0,
λ x1 x2 . x2 = x0 leaving 2 subgoals.
The subproof is completed by applying nat_0.
Apply nat_primrec_0 with
1,
λ x1 x2 . mul_nat x0 x2,
λ x1 x2 . mul_nat x0 x2 = x0.
The subproof is completed by applying mul_nat_1R with x0.