Theorems · Theorem · group theory
DoubleCoset.mk_out_eq_mul
∀ {G : Type u_1} [inst : Group G] (H K : Subgroup G) (g : G),
∃ h k, h ∈ H ∧ k ∈ K ∧ Quotient.out (DoubleCoset.mk H K g) = h * g * k- Defined in
- Mathlib.GroupTheory.DoubleCoset
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 28 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- 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
- Quotient.outstatement and proof · cited by 141
- Subgroup.inv_memproof · cited by 40
- DoubleCoset.Quotientproof · cited by 16
- DoubleCoset.setoidstatement · cited by 13
- eq_mul_inv_of_mul_eqproof · cited by 7
- DoubleCoset.mkstatement and proof · cited by 7
- DoubleCoset.out_eq'proof · cited by 3
- eq_inv_mul_of_mul_eqproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- DoubleCoset.iUnion_quotToDoubleCosetproof · cited by 4