Theorems · Theorem · group theory
AddSubgroup.isComplement_univ_right
∀ {G : Type u_1} [inst : AddGroup G] {S : Set G}, AddSubgroup.IsComplement S Set.univ ↔ ∃ g, S = {g}- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 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
- Set.Elemproof · cited by 7,166
- AddGroupstatement and proof · cited by 4,410
- Set.univstatement and proof · cited by 3,945
- add_neg_cancelproof · cited by 213
- AddSubgroup.IsComplementstatement and proof · cited by 57
- AddSubgroup.mem_topproof · cited by 29
- Set.exists_eq_singleton_iff_nonempty_subsingletonproof · cited by 9
- AddSubgroup.isComplement_singleton_univproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.isComplement'_top_rightproof · cited by 0