Theorems · Theorem · group theory
AddSubgroup.IsComplement.add_eq
∀ {G : Type u_1} [inst : AddGroup G] {S T : Set G}, AddSubgroup.IsComplement S T → S + T = Set.univ- Defined in
- Mathlib.GroupTheory.Complement
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- AddGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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 · cited by 3,945
- Set.addstatement · cited by 338
- Set.eq_univ_of_forallproof · cited by 80
- AddSubgroup.IsComplementstatement and proof · cited by 57
- ExistsUnique.existsproof · cited by 26
- Set.mem_addproof · cited by 25
- AddSubgroup.IsComplement.existsUniqueproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- AddSubgroup.not_isComplement_empty_leftproof · cited by 1
- AddSubgroup.not_isComplement_empty_rightproof · cited by 1
- AddSubgroup.exists_left_transversal_of_leproof · cited by 0
- MeasureTheory.AddSubgroup.index_mul_measureproof · cited by 0
- AddSubgroup.exists_right_transversal_of_leproof · cited by 0