Theorems · Theorem · number theory
isUnit_of_dvd_unit
∀ {α : Type u_1} [inst : CommMonoid α] {x y : α}, x ∣ y → IsUnit y → IsUnit x- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext
- Assumes
- CommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- IsUnitstatement and proof · cited by 1,602
- Dvd.dvd.transproof · cited by 148
- isUnit_iff_dvd_oneproof · cited by 21
Cited by22
Results whose statement or proof uses this declaration.
- Polynomial.isPrimitive_iff_content_eq_oneproof · cited by 4
- exists_bijective_map_powersproof · cited by 3
- not_isUnit_of_not_isUnit_dvdproof · cited by 3
- Irreducible.not_dvd_isUnitproof · cited by 3
- multiplicity_of_isUnit_rightproof · cited by 2
- IsUnit.isRelPrime_leftproof · cited by 2
- IsLocalization.of_le_of_exists_dvdproof · cited by 2
- HomogeneousLocalization.val_awayMapstatement and proof · cited by 2
- HomogeneousLocalization.awayMap_fromZeroRingHomproof · cited by 2
- emultiplicity_of_isUnit_rightproof · cited by 2
- UniqueFactorizationMonoid.normalizedFactors_posproof · cited by 1
- Module.FinitePresentation.exists_lift_equiv_of_isLocalizedModuleproof · cited by 1