∀ {F : Type u_1} {E : Type u_2} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {K : Type u_3}
  [inst_3 : Field K] [inst_4 : Algebra F K] (i : E →ₐ[F] K) {x : E},
  i x ∈ algebraicClosure F K ↔ x ∈ algebraicClosure F E