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Theorems · Theorem · number theory

Units.coe_dvd

∀ {α : Type u_1} [inst : Monoid α] {a : α} {u : αˣ}, ↑u ∣ a

Elements of the unit group of a monoid represented as elements of the monoid divide any element of the monoid.

Defined in
Mathlib.Algebra.Divisibility.Units
Cited by
2 results in Mathlib
Foundations
Depth 10 from the axioms · uses propext
Assumes
Monoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsUnit.dvd · cited by 13IsUnit.dvdlcm_units_coe_left · cited by 3lcm_units_coe_leftMonoid · cited by 3887MonoidUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valUnits.mul_inv_cancel_left · cited by 10Units.mul_inv_cancel_leftUnits.coe_dvdCITED BYCITES

Cites4

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.