Theorems · Theorem · number theory
Units.dvd_mul_right
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {u : αˣ}, a ∣ b * ↑u ↔ a ∣ bIn a monoid, an element a divides an element b iff a divides all associates of b.
- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- Unitsstatement and proof · cited by 2,804
- Units.valstatement and proof · cited by 1,966
- mul_assocproof · cited by 1,667
- dvd_mul_rightproof · cited by 89
- Units.mul_inv_cancel_rightproof · cited by 20
- Dvd.dvd.mul_rightproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- Associated.dvd_iff_dvd_rightproof · cited by 11
- IsUnit.dvd_mul_rightproof · cited by 4
- Units.dvd_mul_leftproof · cited by 3
- dvd_normalize_iffproof · cited by 1