Theorems · Theorem · group theory
DoubleCoset.doubleCoset_eq_of_mem
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G} {a b : G},
b ∈ DoubleCoset.doubleCoset a ↑H ↑K → DoubleCoset.doubleCoset b ↑H ↑K = DoubleCoset.doubleCoset a ↑H ↑K- Defined in
- Mathlib.GroupTheory.DoubleCoset
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 25 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.
Cites10
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
- SetLike.coestatement and proof · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- mul_assocproof · cited by 1,667
- DoubleCoset.doubleCosetstatement and proof · cited by 15
- Set.singleton_mul_singletonproof · cited by 7
- DoubleCoset.mem_doubleCosetproof · cited by 7
- Subgroup.singleton_mul_subgroupproof · cited by 1
- Subgroup.subgroup_mul_singletonproof · cited by 1
Cited by5
Results whose statement or proof uses this declaration.
- DoubleCoset.rel_iffproof · cited by 3
- DoubleCoset.eq_of_not_disjointproof · cited by 1
- DoubleCoset.mem_quotToDoubleCoset_iffproof · cited by 1
- DoubleCoset.iUnion_finset_leftRel_eq_univ_of_leftRelproof · cited by 0
- DoubleCoset.iUnion_finset_rightRel_eq_univ_of_rightRelproof · cited by 0