Theorems · Theorem · group theory
AddSubgroup.isComplement_singleton_left
∀ {G : Type u_1} [inst : AddGroup G] {S : Set G} {g : G}, AddSubgroup.IsComplement {g} S ↔ S = Set.univ- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 60 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.
Cites9
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
- Top.topproof · cited by 9,680
- Set.Elemproof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement and proof · cited by 3,945
- top_le_iffproof · cited by 175
- AddSubgroup.IsComplementstatement and proof · cited by 57
- add_left_cancelproof · cited by 29
- AddSubgroup.isComplement_singleton_univproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.isComplement'_bot_leftproof · cited by 0