∀ {R : Type u} {S : Type v} {ι : Type w} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S]
  {ι' : Type u_1} {T : Type u_2} [inst_3 : CommRing T] [inst_4 : Algebra R T] [inst_5 : Algebra S T]
  [inst_6 : IsScalarTower R S T] (Q : Algebra.Generators S T ι') (P : Algebra.Generators R S ι),
  Q.comp P =
    { val := Sum.elim Q.val (⇑(algebraMap S T) ∘ P.val),
      σ' := fun x =>
        Finsupp.sum (Q.σ x) fun n r =>
          (MvPolynomial.rename Sum.inr) (P.σ r) * (MvPolynomial.monomial (Finsupp.mapDomain Sum.inl n)) 1,
      aeval_val_σ' := ⋯, algebraMap_eq := ⋯ }