Theorems · Theorem · group theory
associated_mul_unit_left
∀ {N : Type u_2} [inst : Monoid N] (a u : N), IsUnit u → Associated (a * u) a- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
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
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- IsUnitstatement and proof · cited by 1,602
- Associatedstatement and proof · cited by 296
- Units.mul_inv_cancel_rightproof · cited by 20
Cited by8
Results whose statement or proof uses this declaration.
- associated_mul_unit_rightproof · cited by 5
- associated_mul_isUnit_left_iffproof · cited by 4
- Irreducible.dvd_iffproof · cited by 4
- associated_unit_mul_leftproof · cited by 4
- IsLocalization.Away.associated_sec_fstproof · cited by 2
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
- prime_mul_iffproof · cited by 0
- UniqueFactorizationMonoid.radical_mul_of_isUnit_rightproof · cited by 0