Theorems · Theorem · group theory
DoubleCoset.iUnion_finset_leftRel_eq_univ_of_leftRel
∀ {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- Defined in
- Mathlib.GroupTheory.DoubleCoset
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Finsetstatement and proof · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.imagestatement and proof · cited by 5,609
- Set.univstatement and proof · cited by 3,945
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- Set.iUnionstatement and proof · cited by 2,483
- MulOppositeproof · cited by 1,135
- MulOpposite.unopproof · cited by 268
- Quotient.outstatement and proof · cited by 141
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