∀ {S : Type u_1} {R : Type u} {M : Type v} [inst : CommSemiring S] [inst_1 : Semiring R] [inst_2 : AddCommMonoid M]
  [inst_3 : Algebra S R] [inst_4 : Module S M] [inst_5 : Module R M] [inst_6 : Module Rᵐᵒᵖ M]
  [inst_7 : SMulCommClass R Rᵐᵒᵖ M] [inst_8 : IsScalarTower S R M] [inst_9 : IsScalarTower S Rᵐᵒᵖ M],
  TrivSqZeroExt.lift (TrivSqZeroExt.inlAlgHom S R M) (↑S (TrivSqZeroExt.inrHom R M)) ⋯ ⋯ ⋯ =
    AlgHom.id S (TrivSqZeroExt R M)