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Proofgold Proof

pf
Apply nat_primrec_S with 1, λ x0 x1 . mul_nat 2 x1, 4, λ x0 x1 . x1 = 32 leaving 2 subgoals.
The subproof is completed by applying nat_4.
Apply unknownprop_18dab10013860d442d73fc2b55cfee57e61b2e3044d2d0c29767dba9e5eb2112 with λ x0 x1 . mul_nat 2 x1 = 32.
The subproof is completed by applying unknownprop_0ea4d9117f5e04c7f1289250df7ab43a5ad0c6cef376e453fd3c5c502e8be6da.