∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : CommSemiring A] [inst_2 : CommRing B]
  [inst_3 : Algebra R A] [inst_4 : Algebra R B] (I : Ideal B) [inst_5 : Algebra A B] (hI : I ^ 2 = ⊥)
  [inst_6 : IsScalarTower R A B] (d : Derivation R A ↥I) (x : A),
  ↑((derivationToSquareZeroEquivLift I hI) d) x = ↑(d x) + (algebraMap A B) x