Theorems · Theorem · group theory
Subgroup.IsComplement.leftQuotientEquiv_apply
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {f : G ⧸ H → G} (hf : ∀ (q : G ⧸ H), ↑(f q) = q) (q : G ⧸ H),
↑(⋯.leftQuotientEquiv q) = f q- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 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.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Equivstatement · cited by 8,337
- Set.Elemstatement · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Set.rangestatement · cited by 4,705
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- QuotientGroup.mkstatement and proof · cited by 196
- Equiv.eq_symm_applyproof · cited by 85
- Subtype.coe_mkproof · cited by 81
- Subgroup.IsComplement.leftQuotientEquivstatement and proof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- Subgroup.transferTransversal_applyproof · cited by 2