∀ {G : Type u} [inst : Group G] (H N : Subgroup G) (hLE : H ≤ N.normalizer),
  QuotientGroup.quotientInfEquivProdNormalizerQuotient H N hLE =
    (QuotientGroup.quotientMulEquivOfEq ⋯).trans
      (QuotientGroup.quotientKerEquivOfSurjective
        ((QuotientGroup.mk' (N.subgroupOf (H ⊔ N))).comp (Subgroup.inclusion ⋯)) ⋯)