Theorems · Theorem · group theory
isUnit_of_mul_isUnit_left
∀ {M : Type u_1} [inst : Monoid M] [IsDedekindFiniteMonoid M] {x y : M}, IsUnit (x * y) → IsUnit x- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 12 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_invproof · cited by 21
Cited by12
Results whose statement or proof uses this declaration.
- IsUnit.mul_iffproof · cited by 8
- Irreducible.squarefreeproof · cited by 6
- Submodule.range_unitsToPicproof · cited by 4
- IsFractionRing.nonZeroDivisors_eq_isUnitproof · cited by 2
- prime_factors_irreducibleproof · cited by 2
- Associated.dvdNotUnit_leftproof · cited by 1
- IsUnit.squarefreeproof · cited by 1
- dvdNotUnit_of_dvdNotUnit_associatedproof · cited by 1
- Polynomial.IsUnitTrinomial.irreducible_of_coprime'proof · cited by 1
- Matrix.inv_kroneckerproof · cited by 0
- mul_mem_nonunits_leftproof · cited by 0