Theorems · Theorem · commutative algebra
DivisorChain.exists_chain_of_prime_pow
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {p : Associates M} {n : ℕ},
n ≠ 0 → Prime p → ∃ c, c 1 = p ∧ StrictMono c ∧ ∀ {r : Associates M}, r ≤ p ^ n ↔ ∃ i, r = c i- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- LT.lt.leproof · cited by 2,189
- LT.lt.ne'proof · cited by 1,417
- CommMonoidWithZerostatement and proof · cited by 913
- pow_oneproof · cited by 894
- StrictMonostatement · cited by 706
- Associatedproof · cited by 296
- Primestatement and proof · cited by 277
- Associatesstatement and proof · cited by 210
- pow_ne_zeroproof · cited by 208
- IsCancelMulZerostatement and proof · cited by 177
- dvd_rflproof · cited by 80
- Prime.ne_zeroproof · cited by 47
Cited by1
Results whose statement or proof uses this declaration.
- pow_image_of_prime_by_factor_orderIso_dvdproof · cited by 1