Theorems · Theorem · commutative algebra
DivisorChain.isPrimePow_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 → IsPrimePow q- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- StrictMonostatement and proof · cited by 706
- UniqueFactorizationMonoidstatement and proof · cited by 279
- Associatesstatement and proof · cited by 210
- IsPrimePowstatement · cited by 77
- zero_lt_iffproof · cited by 29
- irreducible_iff_primeproof · cited by 15
- DivisorChain.second_of_chain_is_irreducibleproof · cited by 3
- DivisorChain.eq_pow_second_of_chain_of_has_chainproof · cited by 2
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