Theorems · Definition · group theory
AddSubmonoid.leftNeg
{M : Type u_1} → [inst : AddMonoid M] → AddSubmonoid M → AddSubmonoid MS.leftNeg is the additive submonoid containing all the left additive inverses of S.
- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- AddMonoidstatement and proof · cited by 2,864
- AddSubmonoidstatement and proof · cited by 1,178
Cited by22
Results whose statement or proof uses this declaration.
- AddSubmonoid.leftNegEquivstatement and proof · cited by 8
- AddSubmonoid.fromLeftNegstatement and proof · cited by 8
- AddSubmonoid.add_fromLeftNegstatement and proof · cited by 5
- AddSubmonoid.leftNegEquiv_applystatement and proof · cited by 2
- AddSubmonoid.fromCommLeftNegstatement · cited by 2
- AddSubmonoid.add_leftNegEquiv_symmstatement · cited by 1
- AddSubmonoid.leftNegEquiv_addstatement and proof · cited by 1
- AddSubmonoid.leftNeg_le_isAddUnitstatement and proof · cited by 1
- AddSubmonoid.leftNeg_leftNeg_lestatement and proof · cited by 1
- AddSubmonoid.addUnit_mem_leftNegstatement · cited by 1
- AddSubmonoid.fromLeftNeg_addstatement and proof · cited by 1
- AddSubmonoid.add_leftNegEquivstatement and proof · cited by 1