Theorems · Theorem · group theory
AddSubmonoid.leftNegEquiv_apply
∀ {M : Type u_1} [inst : AddCommMonoid M] (S : AddSubmonoid M) (hS : S ≤ IsAddUnit.addSubmonoid M) (a : ↥S.leftNeg),
(S.leftNegEquiv hS) a = (↑S.fromCommLeftNeg).toFun a- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 32 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- AddEquivstatement · cited by 1,087
- ZeroHom.toFunstatement · cited by 101
- AddMonoidHom.toZeroHomstatement · cited by 61
- AddSubmonoid.leftNegstatement and proof · cited by 19
- IsAddUnit.addSubmonoidstatement and proof · cited by 16
- AddSubmonoid.leftNegEquivstatement and proof · cited by 8
- AddSubmonoid.fromCommLeftNegstatement · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- AddSubmonoid.leftNegEquiv_addproof · cited by 1
- AddSubmonoid.add_leftNegEquivproof · cited by 1