∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G} {t : Finset (DoubleCoset.Quotient ↑H ↑K)},
  Set.univ ⊆ ⋃ i ∈ t, Quot.mk ⇑(QuotientGroup.leftRel K) '' DoubleCoset.doubleCoset (Quotient.out i) ↑H ↑K →
    ⋃ q ∈ t, DoubleCoset.doubleCoset (Quotient.out q) ↑H ↑K = Set.univ