∀ {F : Type u_1} {E : Type u_2} {K : Type u_3} [inst : Field F] [inst_1 : Field E] [inst_2 : Field K]
  [inst_3 : Algebra F E] [inst_4 : Algebra F K] (carrier : IntermediateField F E) (emb : ↥carrier →ₐ[F] K)
  (carrier_1 : IntermediateField F E) (emb_1 : ↥carrier_1 →ₐ[F] K),
  ({ carrier := carrier, emb := emb } = { carrier := carrier_1, emb := emb_1 }) = (carrier = carrier_1 ∧ emb ≍ emb_1)