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Proofgold Proof

pf
Let x0 of type ι be given.
Let x1 of type ι be given.
Assume H0: even_nat x0.
Assume H1: odd_nat x1.
Apply H0 with odd_nat (add_SNo x0 x1).
Assume H2: x0 ∈ omega.
Assume H3: ∃ x2 . and (x2 ∈ omega) (x0 = mul_nat 2 x2).
Apply H1 with odd_nat (add_SNo x0 x1).
Assume H4: x1 ∈ omega.
Assume H5: ∀ x2 . x2 ∈ omega ⟶ x1 = mul_nat 2 x2 ⟶ ∀ x3 : ο . x3.
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 unknownprop_414262d1e5b2db2262078b4488f97bc47bc9ca3b09dbbe687ba5589aa53bd3b9 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
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