Theorems · Theorem · group theory
IsAddUnit.add_left_inj
∀ {M : Type u_1} [inst : AddMonoid M] {a b c : M}, IsAddUnit a → (b + a = c + a ↔ b = c)- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- AddMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- AddMonoidstatement and proof · cited by 2,864
- AddUnitsproof · cited by 325
- AddUnits.valproof · cited by 248
- IsAddUnitstatement and proof · cited by 215
- AddUnits.add_left_injproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- IsAddUnit.add_right_cancelproof · cited by 2
- IsAddUnit.sub_eq_sub_iffproof · cited by 2
- AddSubmonoid.LocalizationMap.map_isAddRegularproof · cited by 1
- IsAddUnit.add_eq_rightproof · cited by 1
- AddCommute.sub_eq_sub_iff_of_isAddUnitproof · cited by 1
- AddSubmonoid.LocalizationMap.map_injective_of_surjOn_or_injectiveproof · cited by 1
- AddSubmonoid.LocalizationMap.epic_of_localizationMapproof · cited by 0
- AddSubmonoid.LocalizationMap.mk'_eq_of_sameproof · cited by 0