Proofgold Proof

pf
Let x0 of type ι be given. Assume H0: RealsStruct x0. Apply Field_of_RealsStruct_0 with x0, λ x1 x2 . ∀ x3 x4 . nIn x4 x1 ⟶ Field_div (Field_of_RealsStruct x0) x3 x4 = 0. Apply Field_div_undef2 with Field_of_RealsStruct x0. Apply Field_Field_of_RealsStruct with x0. The subproof is completed by applying H0. ■