Theorems · Theorem · group theory
Irreducible.dvd_iff
∀ {M : Type u_1} [inst : Monoid M] {x y : M}, Irreducible x → (y ∣ x ↔ IsUnit y ∨ Associated x y)- Defined in
- Mathlib.Algebra.GroupWithZero.Associated
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Irreduciblestatement and proof · cited by 496
- Associatedstatement and proof · cited by 296
- Associated.symmproof · cited by 87
- Associated.dvdproof · cited by 38
- Irreducible.isUnit_or_isUnitproof · cited by 28
- IsUnit.dvdproof · cited by 13
- associated_mul_unit_leftproof · cited by 8
Cited by4
Results whose statement or proof uses this declaration.
- Irreducible.associated_of_dvdproof · cited by 6
- Irreducible.isRelPrime_iff_not_dvdproof · cited by 4
- Irreducible.isUnit_iff_not_associated_of_dvdproof · cited by 1
- Associates.one_or_eq_of_le_of_primeproof · cited by 0