Proofgold Proof

The subproof is completed by applying and7I with Field x0, Field x1, x2 ∈ setexp (field0 x1) (field0 x0), ap x2 (field3 x0) = field3 x1, ap x2 (field4 x0) = field4 x1, ∀ x3 . x3 ∈ field0 x0 ⟶ ∀ x4 . x4 ∈ field0 x0 ⟶ ap x2 (field1b x0 x3 x4) = field1b x1 (ap x2 x3) (ap x2 x4), ∀ x3 . x3 ∈ field0 x0 ⟶ ∀ x4 . x4 ∈ field0 x0 ⟶ ap x2 (field2b x0 x3 x4) = field2b x1 (ap x2 x3) (ap x2 x4).