Theorems · Theorem · group theory
AddSubmonoid.leftNegEquiv_add
∀ {M : Type u_1} [inst : AddCommMonoid M] (S : AddSubmonoid M) (hS : S ≤ IsAddUnit.addSubmonoid M) (x : ↥S.leftNeg),
↑((S.leftNegEquiv hS) x) + ↑x = 0- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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.
- DFunLike.coestatement · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- AddEquivstatement · cited by 1,087
- AddSubmonoid.leftNegstatement and proof · cited by 19
- IsAddUnit.addSubmonoidstatement and proof · cited by 16
- AddSubmonoid.leftNegEquivstatement · cited by 8
- AddSubmonoid.leftNegEquiv_applyproof · cited by 2
- AddSubmonoid.fromLeftNeg_addproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- AddSubmonoid.add_leftNegEquiv_symmproof · cited by 1