Theorems · Theorem · commutative algebra
DivisorChain.element_of_chain_eq_pow_second_of_chain
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [UniqueFactorizationMonoid M] {q r : Associates M} {n : ℕ},
n ≠ 0 →
∀ {c : Fin (n + 1) → Associates M},
StrictMono c → (∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i) → r ∣ q → q ≠ 0 → ∃ i, r = c 1 ^ ↑i- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 77 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites31
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.univproof · cited by 3,473
- Multisetproof · cited by 2,627
- Finset.cardproof · cited by 2,327
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.imageproof · cited by 910
- StrictMonostatement and proof · cited by 706
- Multiset.prodproof · cited by 528
- Multiset.cardproof · cited by 375
- Associatedproof · cited by 296
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- UniqueFactorizationMonoid.normalizedFactorsproof · cited by 151
Cited by1
Results whose statement or proof uses this declaration.
- DivisorChain.eq_pow_second_of_chain_of_has_chainproof · cited by 2