∀ {k : Type u_2} {K : Type u_1} [inst : Field k] [inst_1 : Field K] [inst_2 : Algebra k K]
  (L : FiniteGaloisIntermediateField k K)
  (x x_1 : ↑(ProfiniteGrp.limit (InfiniteGalois.asProfiniteGaloisGroupFunctor k K)).toProfinite.toTop),
  ↑(x * x_1) (Opposite.op L) = ↑(x * x_1) (Opposite.op L)