Theorems · Theorem · group theory
IsUnit.mul_iff
∀ {M : Type u_1} [inst : Monoid M] [IsDedekindFiniteMonoid M] {x y : M}, IsUnit (x * y) ↔ IsUnit x ∧ IsUnit y- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- MonoidIsDedekindFiniteMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- IsUnitstatement and proof · cited by 1,602
- IsUnit.mulproof · cited by 32
- IsDedekindFiniteMonoidstatement and proof · cited by 23
- isUnit_of_mul_isUnit_leftproof · cited by 12
- isUnit_of_mul_isUnit_rightproof · cited by 8
Cited by8
Results whose statement or proof uses this declaration.
- Int.eq_one_or_neg_one_of_mul_eq_neg_one'proof · cited by 2
- IsLocalization.isLocalization_of_is_exists_mul_memproof · cited by 2
- Polynomial.UniversalCoprimeFactorizationRing.isCoprime_factor₁_factor₂proof · cited by 1
- IsLocalization.localization_localization_map_unitsproof · cited by 1
- List.prod_isUnit_iffproof · cited by 1
- WeierstrassCurve.twoTorsionPolynomial_discr_isUnitproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueFieldproof · cited by 1
- Polynomial.resultant_eq_zero_iffproof · cited by 0