∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (pb : PowerBasis R S)
  (I : Ideal R) (x : R),
  ((Ideal.map (algebraMap R S) I).quotientEquiv (Ideal.map (AdjoinRoot.of (minpoly R pb.gen)) I)
        (AdjoinRoot.equiv' (minpoly R pb.gen) pb ⋯ ⋯).symm.toRingEquiv ⋯)
      ((algebraMap R (S ⧸ Ideal.map (algebraMap R S) I)) x) =
    (algebraMap R (AdjoinRoot (minpoly R pb.gen) ⧸ Ideal.map (AdjoinRoot.of (minpoly R pb.gen)) I)) x