Theorems · Theorem · group theory
AddSubmonoid.fromLeftNeg_eq_iff
∀ {M : Type u_1} [inst : AddCommMonoid M] (S : AddSubmonoid M) (a : ↥S.leftNeg) (b : M),
↑(S.fromLeftNeg a) = b ↔ ↑a + b = 0- Defined in
- Mathlib.GroupTheory.Submonoid.Inverses
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 25 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddCommMonoidstatement and proof · cited by 12,281
- AddSubmonoidstatement and proof · cited by 1,178
- Subtype.propproof · cited by 505
- AddSubmonoid.leftNegstatement and proof · cited by 19
- AddSubmonoid.fromLeftNegstatement · cited by 8
- IsAddUnit.add_right_injproof · cited by 7
- AddSubmonoid.add_fromLeftNegproof · cited by 5
- AddSubmonoid.leftNeg_le_isAddUnitproof · cited by 1
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