Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H1 with
odd_nat (mul_nat x0 x1).
Assume H3:
∀ x2 . x2 ∈ omega ⟶ x1 = mul_nat 2 x2 ⟶ ∀ x3 : ο . x3.
Apply odd_nat_iff_odd_mul_nat with
x0,
x1,
odd_nat (mul_nat x0 x1) leaving 3 subgoals.
The subproof is completed by applying H0.
Apply omega_nat_p with
x1.
The subproof is completed by applying H2.
Apply H4.
The subproof is completed by applying H1.