Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.squarefree_iff_nodup_normalizedFactors
∀ {R : Type u_1} [inst : CommMonoidWithZero R] [inst_1 : UniqueFactorizationMonoid R] [inst_2 : NormalizationMonoid R]
{x : R}, x ≠ 0 → (Squarefree x ↔ (UniqueFactorizationMonoid.normalizedFactors x).Nodup)- Defined in
- Mathlib.Algebra.Squarefree.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- ENatproof · cited by 4,985
- Nat.cast_oneproof · cited by 2,501
- Nontrivialproof · cited by 2,416
- IsUnitproof · cited by 1,602
- eq_or_neproof · cited by 1,117
- le_transproof · cited by 985
- CommMonoidWithZerostatement and proof · cited by 913
- Irreducibleproof · cited by 496
- Multiset.countproof · cited by 302
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- emultiplicityproof · cited by 156
Cited by3
Results whose statement or proof uses this declaration.
- Nat.squarefree_iff_nodup_primeFactorsListproof · cited by 4
- UniqueFactorizationMonoid.normalizedFactors_nodupproof · cited by 2
- Nat.divisors_filter_squarefreeproof · cited by 1