Theorems · Definition · group theory
AddSubgroup.IsComplement.leftQuotientEquiv
{G : Type u_1} → [inst : AddGroup G] → {H : AddSubgroup G} → {S : Set G} → AddSubgroup.IsComplement S ↑H → G ⧸ H ≃ ↑SA left transversal is in bijection with left cosets.
- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 74 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Equivstatement · cited by 8,337
- SetLike.coestatement and proof · cited by 8,199
- Set.Elemstatement · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- Equiv.symmproof · cited by 3,681
- AddSubgroupstatement and proof · cited by 3,232
- HasQuotient.Quotientstatement · cited by 2,301
- Set.domRestrictproof · cited by 383
- QuotientAddGroup.mkproof · cited by 348
- Equiv.ofBijectiveproof · cited by 70
- AddSubgroup.IsComplementstatement and proof · cited by 57
Cited by10
Results whose statement or proof uses this declaration.
- AddSubgroup.leftTransversals.diffproof · cited by 5
- AddSubgroup.IsComplement.toLeftFunproof · cited by 4
- AddSubgroup.IsComplement.finite_left_iffproof · cited by 3
- AddSubgroup.leftCoset_cover_filter_FiniteIndex_auxproof · cited by 3
- AddSubgroup.leftTransversals.diff_add_diffproof · cited by 3
- AddSubgroup.leftTransversals.vadd_diff_vaddproof · cited by 1
- AddSubgroup.vadd_leftQuotientEquivstatement · cited by 1
- AddSubgroup.IsComplement.quotientAddGroupMk_leftQuotientEquivstatement and proof · cited by 1
- AddSubgroup.vadd_apply_eq_vadd_apply_neg_vaddstatement and proof · cited by 1
- AddSubgroup.IsComplement.leftQuotientEquiv_applystatement and proof · cited by 0