Let x0 of type ι be given.
Let x1 of type ι be given.
Apply H0 with
odd_nat (add_SNo x0 x1).
Assume H3:
∀ x2 . x2 ∈ omega ⟶ x0 = mul_nat 2 x2 ⟶ ∀ x3 : ο . x3.
Apply H1 with
odd_nat (add_SNo x0 x1).
Apply add_nat_add_SNo with
x0,
x1,
λ x2 x3 . odd_nat x2 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Apply add_nat_com with
x0,
x1,
λ x2 x3 . odd_nat x3 leaving 3 subgoals.
Apply omega_nat_p with
x0.
The subproof is completed by applying H2.
Apply omega_nat_p with
x1.
The subproof is completed by applying H4.
Apply unknownprop_414262d1e5b2db2262078b4488f97bc47bc9ca3b09dbbe687ba5589aa53bd3b9 with
x1,
x0 leaving 2 subgoals.
The subproof is completed by applying H1.
The subproof is completed by applying H0.