Theorems · Theorem · group theory
AddSubgroup.isComplement_univ_singleton
∀ {G : Type u_1} [inst : AddGroup G] {g : G}, AddSubgroup.IsComplement Set.univ {g}- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · 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
- neg_add_cancel_rightproof · cited by 75
- AddSubgroup.IsComplementstatement · cited by 57
- add_right_cancelproof · cited by 23
Cited by3
Results whose statement or proof uses this declaration.
- AddSubgroup.isComplement_univ_leftproof · cited by 1
- AddSubgroup.isComplement_singleton_rightproof · cited by 1
- AddSubgroup.isComplement'_top_botproof · cited by 0