Theorems · Theorem · group theory
DoubleCoset.eq
∀ {G : Type u_1} [inst : Group G] (H K : Subgroup G) (a b : G),
DoubleCoset.mk H K a = DoubleCoset.mk H K b ↔ ∃ h ∈ H, ∃ k ∈ K, b = h * a * k- Defined in
- Mathlib.GroupTheory.DoubleCoset
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 27 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.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- DoubleCoset.Quotientstatement · cited by 16
- DoubleCoset.mkstatement · cited by 7
- DoubleCoset.rel_iffproof · cited by 3
- DoubleCoset.eq''proof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- DoubleCoset.mk_eq_of_doubleCoset_eqproof · cited by 2
- DoubleCoset.mk_out_eq_mulproof · cited by 1
- DoubleCoset.mem_quotToDoubleCoset_iffproof · cited by 1