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Proofgold Proof

pf
Let x0 of type ι be given.
Assume H0: Field x0.
Let x1 of type ι be given.
Assume H1: nIn x1 (field0 x0).
Apply If_i_0 with x1ap x0 0, explicit_Field_minus (ap x0 0) (ap x0 3) (ap x0 4) (decode_b (ap x0 1)) (decode_b (ap x0 2)) x1, 0.
The subproof is completed by applying H1.