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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: even_nat x1.
Apply H0 with even_nat (add_SNo x0 x1).
Assume H2: x0 ∈ omega.
Assume H3: ∃ x2 . and (x2 ∈ omega) (x0 = mul_nat 2 x2).
Apply H1 with even_nat (add_SNo x0 x1).
Assume H4: x1 ∈ omega.
Assume H5: ∃ x2 . and (x2 ∈ omega) (x1 = mul_nat 2 x2).
Apply add_nat_add_SNo with x0, x1, λ x2 x3 . even_nat x2 leaving 3 subgoals.
The subproof is completed by applying H2.
The subproof is completed by applying H4.
Apply unknownprop_209520ddb6996883d29652b83315cacb601bd4047ab755a61e6bc2c1bd94b0c5 with x0, x1 leaving 2 subgoals.
The subproof is completed by applying H0.
The subproof is completed by applying H1.
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