apply isInf.lift (fun H H' ↦ (Subgroup.ext_iff H H').2)
G : Type
inst✝ : Group G
s : Set (Subgroup G)
H : Subgroup G
⊢ H ∈ lowerBounds s ↔ H ≤ SubgroupInf s
case hy
G : Type
inst✝ : Group G
s : Set (Subgroup G)
H : Subgroup G
⊢ isInf ((fun H => H.carrier) '' s) (SubgroupInf s).carrier