Theorems · Theorem · group theory
DoubleCoset.iUnion_quotToDoubleCoset
∀ {G : Type u_1} [inst : Group G] (H K : Subgroup G), ⋃ q, DoubleCoset.quotToDoubleCoset H K q = Set.univ- Defined in
- Mathlib.GroupTheory.DoubleCoset
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.univstatement · cited by 3,945
- Subgroupstatement and proof · cited by 3,593
- one_mulproof · cited by 2,841
- Set.iUnionstatement · cited by 2,483
- Set.extproof · cited by 2,266
- Quotient.outproof · cited by 141
- inv_mul_cancelproof · cited by 107
- mul_inv_cancel_rightproof · cited by 53
- Subgroup.inv_memproof · cited by 40
Cited by4
Results whose statement or proof uses this declaration.
- DoubleCoset.finite_quotient_iff_exists_finset_iUnion_eq_univproof · cited by 0
- DoubleCoset.iUnion_image_mk_leftRelproof · cited by 0
- DoubleCoset.iUnion_image_mk_rightRelproof · cited by 0
- DoubleCoset.union_quotToDoubleCosetproof · cited by 0