Theorems · Theorem · group theory
associated_mul_isUnit_left_iff
∀ {N : Type u_2} [inst : Monoid N] {a u b : N}, IsUnit u → (Associated (a * u) b ↔ Associated a b)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 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
- IsUnitstatement and proof · cited by 1,602
- Associatedstatement · cited by 296
- Associated.transproof · cited by 22
- associated_mul_unit_leftproof · cited by 8
- associated_mul_unit_rightproof · cited by 5
Cited by4
Results whose statement or proof uses this declaration.
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- associated_isUnit_mul_left_iffproof · cited by 2
- associated_mul_isUnit_right_iffproof · cited by 1
- associated_mul_unit_left_iffproof · cited by 0