Theorems · Theorem · commutative algebra
DivisorChain.eq_pow_second_of_chain_of_has_chain
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [UniqueFactorizationMonoid M] {q : Associates M} {n : ℕ},
n ≠ 0 →
∀ {c : Fin (n + 1) → Associates M},
StrictMono c → (∀ {r : Associates M}, r ≤ q ↔ ∃ i, r = c i) → q ≠ 0 → q = c 1 ^ n- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finset.univproof · cited by 3,473
- CommMonoidWithZerostatement and proof · cited by 913
- Finset.imageproof · cited by 910
- StrictMonostatement and proof · cited by 706
- Finset.mem_univproof · cited by 361
- Associatedproof · cited by 296
- Function.Injective.injOnproof · cited by 280
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Primeproof · cited by 277
- Associatesstatement and proof · cited by 210
- Finset.card_le_cardproof · cited by 118
- Finset.mem_imageproof · cited by 105
Cited by2
Results whose statement or proof uses this declaration.
- pow_image_of_prime_by_factor_orderIso_dvdproof · cited by 1
- DivisorChain.isPrimePow_of_has_chainproof · cited by 0