Theorems · Theorem · group theory
IsUnit.mul_left_inj
∀ {M : Type u_1} [inst : Monoid M] {a b c : M}, IsUnit a → (b * a = c * a ↔ b = c)- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 20 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- Monoid
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.
- Monoidstatement and proof · cited by 3,887
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Units.mul_left_injproof · cited by 8
Cited by20
Results whose statement or proof uses this declaration.
- IsUnit.mul_right_cancelproof · cited by 6
- IsLocalization.isLocalization_of_submonoid_leproof · cited by 5
- IsPrimitiveRoot.pow_injproof · cited by 4
- IsUnit.div_eq_div_iffproof · cited by 3
- Module.IsLocalRing.linearIndependent_of_flatproof · cited by 2
- Submonoid.LocalizationMap.map_isRegularproof · cited by 2
- Commute.div_eq_div_iff_of_isUnitproof · cited by 2
- IsUnit.isSelfAdjoint_conjugate_iffproof · cited by 1
- Localization.existsUnique_algebraMap_eq_of_span_eq_topproof · cited by 1
- Submonoid.LocalizationMap.mk'_eq_zero_iffproof · cited by 1
- IsUnit.mul_eq_rightproof · cited by 1
- Submonoid.LocalizationMap.map_injective_of_surjOn_or_injectiveproof · cited by 1