Theorems · Theorem · group theory
isUnit_of_mul_isUnit_right
∀ {M : Type u_1} [inst : Monoid M] [IsDedekindFiniteMonoid M] {x y : M}, IsUnit (x * y) → IsUnit y- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses no axioms
- Assumes
- MonoidIsDedekindFiniteMonoid
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
- mul_assocproof · cited by 1,667
- IsUnitstatement and proof · cited by 1,602
- IsDedekindFiniteMonoidstatement and proof · cited by 23
- isUnit_iff_exists_inv'proof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- IsUnit.mul_iffproof · cited by 8
- Polynomial.IsPrimitive.irreducible_iff_irreducible_map_fraction_mapproof · cited by 4
- Polynomial.isUnit_or_eq_zero_of_isUnit_integerNormalization_primPartproof · cited by 1
- HahnSeries.isUnit_of_isUnit_leadingCoeff_AddUnitOrderproof · cited by 1
- Matrix.inv_kroneckerproof · cited by 0
- HahnSeries.isUnit_iffproof · cited by 0
- Polynomial.Monic.irreducible_of_irreducible_map_of_isPrime_nilradicalproof · cited by 0
- mul_mem_nonunits_rightproof · cited by 0