Theorems · Theorem · group theory
IsUnit.mul_right_inj
∀ {M : Type u_1} [inst : Monoid M] {a b c : M}, IsUnit a → (a * b = a * c ↔ b = c)- Defined in
- Mathlib.Algebra.Group.Units.Basic
- Cited by
- 13 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_right_injproof · cited by 4
Cited by13
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.eq_iff_existsproof · cited by 9
- IsUnit.mul_left_cancelproof · cited by 6
- LinearIndependent.of_isLocalizedModuleproof · cited by 2
- one_sub_invOf_twoproof · cited by 1
- Submonoid.IsLocalizationMap.map_oneproof · cited by 1
- IsUnit.mul_eq_leftproof · cited by 1
- IsUnit.isSelfAdjoint_conjugate_iffproof · cited by 1
- Commute.inv_mul_eq_inv_mul_iff_of_isUnitproof · cited by 1
- Polynomial.IsUnitTrinomial.irreducible_aux2proof · cited by 1
- AlgebraicGeometry.RingedSpace.isUnit_of_isUnit_germproof · cited by 1
- Submonoid.fromLeftInv_eq_iffproof · cited by 0
- IsStronglyTranscendental.of_isLocalization_leftproof · cited by 0