Theorems · Theorem · group theory
Subgroup.exists_isComplement_left
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) (g : G), ∃ S, Subgroup.IsComplement S ↑H ∧ g ∈ S- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 75 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- SetLike.coestatement · cited by 8,199
- Groupstatement and proof · cited by 6,238
- Set.rangeproof · cited by 4,705
- Subgroupstatement and proof · cited by 3,593
- HasQuotient.Quotientproof · cited by 2,301
- Function.updateproof · cited by 502
- Function.update_selfproof · cited by 201
- QuotientGroup.mkproof · cited by 196
- Quotient.outproof · cited by 141
- Quotient.mk''proof · cited by 132
- Subgroup.IsComplementstatement · cited by 94
Cited by3
Results whose statement or proof uses this declaration.
- Subgroup.exists_leftTransversal_of_FiniteIndexproof · cited by 1
- MeasureTheory.Subgroup.index_mul_measureproof · cited by 0
- Subgroup.exists_left_transversal_of_leproof · cited by 0