∀ (K : Type u_1) [inst : CommRing K] (p : ℕ) [inst_1 : Fact (Nat.Prime p)] [inst_2 : CharP K p] (L : Type u_2)
  [inst_3 : CommSemiring L] [inst_4 : CharP L p] [inst_5 : PerfectRing L p] (f : K →+* L) (x y : PerfectClosure K p),
  (x * y).liftOn (fun x => (⇑(frobeniusEquiv L p).symm)^[x.1] (f x.2)) ⋯ =
    x.liftOn (fun x => (⇑(frobeniusEquiv L p).symm)^[x.1] (f x.2)) ⋯ *
      y.liftOn (fun x => (⇑(frobeniusEquiv L p).symm)^[x.1] (f x.2)) ⋯