Theorems · Theorem · number theory
Units.mul_right_dvd
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {u : αˣ}, a * ↑u ∣ b ↔ a ∣ bIn a monoid, an element a divides an element b iff all associates of a divide b.
- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 9 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by7
Results whose statement or proof uses this declaration.
- Associated.dvd_iff_dvd_leftproof · cited by 6
- IsUnit.mul_right_dvdproof · cited by 4
- Polynomial.separable_iff_derivative_ne_zeroproof · cited by 2
- Units.mul_left_dvdproof · cited by 1
- normalize_dvd_iffproof · cited by 1
- Polynomial.associated_of_dvd_of_natDegree_le_of_leadingCoeffproof · cited by 1
- Associates.isPrimal_mkproof · cited by 0