Theorems · Theorem · group theory
AddSubmonoid.leftNegEquiv_symm_eq_neg
∀ {M : Type u_1} [inst : AddCommGroup M] (S : AddSubmonoid M) (hS : S ≤ IsAddUnit.addSubmonoid M) (x : ↥S),
↑((S.leftNegEquiv hS).symm x) = -↑x- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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Cites11
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
- AddCommGroupstatement and proof · cited by 12,871
- AddSubmonoidstatement and proof · cited by 1,178
- AddEquivstatement · cited by 1,087
- AddEquiv.symmstatement and proof · cited by 530
- add_neg_cancelproof · cited by 213
- add_right_injproof · cited by 71
- AddSubmonoid.leftNegstatement · cited by 19
- IsAddUnit.addSubmonoidstatement and proof · cited by 16
- AddSubmonoid.leftNegEquivstatement and proof · cited by 8
- AddSubmonoid.add_leftNegEquiv_symmproof · cited by 1
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