Theorems · Theorem · commutative algebra
UniqueFactorizationMonoid.normalizedFactors_pos
∀ {α : Type u_1} [inst : CommMonoidWithZero α] [inst_1 : NormalizationMonoid α] [inst_2 : UniqueFactorizationMonoid α]
(x : α), x ≠ 0 → (0 < UniqueFactorizationMonoid.normalizedFactors x ↔ ¬IsUnit x)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Multisetstatement · cited by 2,627
- IsUnitstatement and proof · cited by 1,602
- LT.lt.ne'proof · cited by 1,417
- CommMonoidWithZerostatement and proof · cited by 913
- UniqueFactorizationMonoidstatement and proof · cited by 279
- NormalizationMonoidstatement and proof · cited by 165
- UniqueFactorizationMonoid.normalizedFactorsstatement and proof · cited by 151
- bot_lt_iff_ne_botproof · cited by 57
- Prime.not_isUnitproof · cited by 29
- UniqueFactorizationMonoid.prime_of_normalized_factorproof · cited by 23
- isUnit_of_dvd_unitproof · cited by 22
- UniqueFactorizationMonoid.dvd_of_mem_normalizedFactorsproof · cited by 20
Cited by1
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.normalizedFactors_eq_zero_iffproof · cited by 2