Theorems · Theorem · group theory
Subgroup.exists_isComplement_right
∀ {G : Type u_1} [inst : Group G] (H : Subgroup G) (g : G), ∃ T, Subgroup.IsComplement (↑H) T ∧ g ∈ T- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 72 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.
- 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
- Function.updateproof · cited by 502
- Function.update_selfproof · cited by 201
- Quotient.outproof · cited by 141
- Quotient.mk''proof · cited by 132
- Subgroup.IsComplementstatement · cited by 94
- QuotientGroup.rightRelproof · cited by 44
- Quotient.out_eq'proof · cited by 35
Cited by4
Results whose statement or proof uses this declaration.
- Monoid.PushoutI.NormalWord.transversal_nonemptyproof · cited by 3
- ProperlyDiscontinuousSMul.ofFiniteRelIndexproof · cited by 1
- Subgroup.exists_finset_card_le_mulproof · cited by 1
- Subgroup.exists_right_transversal_of_leproof · cited by 0