∀ {S : Type u_1} [inst : CommRing S] (I : Ideal S) [inst_1 : IsAdicComplete I S] (x : S),
  (↑(AdicCompletion.ofLinearEquiv I S)).toFun ((algebraMap S S) x) =
    (↑(AdicCompletion.ofLinearEquiv I S)).toFun ((algebraMap S S) x)