Theorems · Theorem · commutative algebra
dvd_of_emultiplicity_pos
∀ {α : Type u_1} [inst : Monoid α] {a b : α}, 0 < emultiplicity a b → a ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 36 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatstatement · cited by 4,985
- Monoidstatement and proof · cited by 3,887
- pow_oneproof · cited by 894
- emultiplicitystatement and proof · cited by 156
- Order.add_one_le_of_ltproof · cited by 13
- pow_dvd_of_le_emultiplicityproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- dvd_of_multiplicity_posproof · cited by 1