Theorems · Theorem · commutative algebra
not_pow_dvd_of_emultiplicity_lt
∀ {α : Type u_1} [inst : Monoid α] {a b : α} {m : ℕ}, emultiplicity a b < ↑m → ¬a ^ m ∣ b- Defined in
- Mathlib.RingTheory.Multiplicity
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 34 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
- emultiplicitystatement and proof · cited by 156
- Dvd.dvd.transproof · cited by 148
- FiniteMultiplicityproof · cited by 73
- pow_dvd_powproof · cited by 56
Cited by3
Results whose statement or proof uses this declaration.
- emultiplicity_eq_coeproof · cited by 9
- le_emultiplicity_of_pow_dvdproof · cited by 6
- FiniteMultiplicity.not_pow_dvd_of_multiplicity_ltproof · cited by 5