∀ (R : Type u_2) {A : Type u_1} [inst : CommSemiring R] [inst_1 : CommRing A] [inst_2 : Algebra R A] (I J : Ideal A)
  (x : R),
  (↑↑(DoubleQuot.quotLeftToQuotSup I J)).toFun ((algebraMap R (A ⧸ I)) x) =
    (↑↑(DoubleQuot.quotLeftToQuotSup I J)).toFun ((algebraMap R (A ⧸ I)) x)