Theorems · Theorem · group theory
AddSubgroup.not_isComplement_empty_right
∀ {G : Type u_1} [inst : AddGroup G] {S : Set G}, ¬AddSubgroup.IsComplement S ∅- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 25 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.
Cites8
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
- AddGroupstatement and proof · cited by 4,410
- Set.univproof · cited by 3,945
- AddSubgroup.IsComplementstatement and proof · cited by 57
- Set.univ_eq_empty_iffproof · cited by 13
- not_isEmpty_of_nonemptyproof · cited by 8
- AddSubgroup.IsComplement.add_eqproof · cited by 5
- Set.add_emptyproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- AddSubgroup.IsComplement.nonempty_rightproof · cited by 0