∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] {x : S} {I : Ideal R}
  (hx : Ideal.comap (algebraMap R S) (conductor R x) ⊔ I = ⊤) (h_alg : Function.Injective ⇑(algebraMap (↥R[x]) S)),
  quotAdjoinEquivQuotMap hx h_alg = quotAdjoinEquivQuotMap hx h_alg