Theorems · Definition · group theory
Subgroup.IsComplement.toLeftFun
{G : Type u_1} → [inst : Group G] → {H : Subgroup G} → {S : Set G} → Subgroup.IsComplement S ↑H → G → ↑SA left transversal can be viewed as a function mapping each element of the group to the chosen representative from that left coset.
- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 76 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.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · cited by 53,352
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Subgroupstatement and proof · cited by 3,593
- Quotient.mk''proof · cited by 132
- Subgroup.IsComplementstatement and proof · cited by 94
- Subgroup.IsComplement.leftQuotientEquivproof · cited by 17
Cited by4
Results whose statement or proof uses this declaration.
- Subgroup.IsComplement.inv_toLeftFun_mul_memstatement · cited by 3
- Subgroup.smul_toLeftFunstatement · cited by 1
- Subgroup.exists_leftTransversal_of_FiniteIndexproof · cited by 1
- Subgroup.IsComplement.inv_mul_toLeftFun_memstatement and proof · cited by 0