Theorems · Theorem · number theory
IsUnit.dvd
∀ {α : Type u_1} [inst : Monoid α] {a u : α}, IsUnit u → u ∣ aUnits of a monoid divide any element of the monoid.
- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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
- Units.coe_dvdproof · cited by 2
Cited by13
Results whose statement or proof uses this declaration.
- isUnit_iff_dvd_oneproof · cited by 21
- Polynomial.associated_of_dvd_of_natDegree_leproof · cited by 4
- Irreducible.dvd_iffproof · cited by 4
- FiniteMultiplicity.not_isUnitproof · cited by 3
- AddSubgroup.index_dvd_two_iffproof · cited by 2
- divRadical_dvd_derivativeproof · cited by 1
- pow_dvd_of_mul_eq_powproof · cited by 1
- Squarefree.pow_dvd_of_pow_dvdproof · cited by 1
- Polynomial.Monic.C_dvd_iff_isUnitproof · cited by 1
- AddMonoid.exponent_eq_prime_iffproof · cited by 1
- exists_squarefree_dvd_pow_of_ne_zeroproof · cited by 1
- IsUnit.isPrimalproof · cited by 0