Theorems · Theorem · group theory
DoubleCoset.mem_quotToDoubleCoset_iff
∀ {G : Type u_1} [inst : Group G] {H K : Subgroup G} (i : DoubleCoset.Quotient ↑H ↑K) (a : G),
a ∈ DoubleCoset.quotToDoubleCoset H K i ↔ DoubleCoset.mk H K a = i- Defined in
- Mathlib.GroupTheory.DoubleCoset
- Cited by
- 1 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.
Cites14
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
- Subgroupstatement and proof · cited by 3,593
- Quotient.outproof · cited by 141
- Quotient.out_eqproof · cited by 27
- DoubleCoset.Quotientstatement and proof · cited by 16
- DoubleCoset.mem_doubleCosetproof · cited by 7
- DoubleCoset.mkstatement and proof · cited by 7
- DoubleCoset.quotToDoubleCosetstatement and proof · cited by 6
- DoubleCoset.doubleCoset_eq_of_memproof · cited by 5
- DoubleCoset.out_eq'proof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- DoubleCoset.finite_quotient_iff_exists_finset_iUnion_eq_univproof · cited by 0