Theorems · Theorem · group theory
Subgroup.isComplement_range_left
∀ {G : Type u_1} [inst : Group G] {H : Subgroup G} {f : G ⧸ H → G},
(∀ (q : G ⧸ H), ↑(f q) = q) → Subgroup.IsComplement (Set.range f) ↑H- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 74 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- SetLike.coestatement · cited by 8,199
- Set.Elemproof · cited by 7,166
- Groupstatement and proof · cited by 6,238
- Set.rangestatement and proof · cited by 4,705
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientstatement and proof · cited by 2,301
- Set.domRestrictproof · cited by 383
- QuotientGroup.mkstatement and proof · cited by 196
- Subgroup.IsComplementstatement · cited by 94
- Subgroup.isComplement_subgroup_right_iff_bijectiveproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Subgroup.exists_isComplement_leftproof · cited by 3
- Subgroup.IsComplement.leftQuotientEquiv_applystatement and proof · cited by 1