Theorems · Theorem · commutative algebra
DivisorChain.eq_second_of_chain_of_prime_dvd
∀ {M : Type u_1} [inst : CommMonoidWithZero M] [IsCancelMulZero M] {p 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) → Prime p → r ∣ q → p ∣ r → p = c 1- Defined in
- Mathlib.RingTheory.ChainOfDivisors
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Primestatement and proof · cited by 277
- Associatesstatement and proof · cited by 210
- IsCancelMulZerostatement and proof · cited by 177
- Prime.irreducibleproof · cited by 54
- dvd_transproof · cited by 50
- Prime.not_isUnitproof · cited by 29
- Fin.le_iff_val_le_valproof · cited by 15
- eq_of_le_of_not_lt'proof · cited by 6
- Associates.dvdNotUnit_iff_ltproof · cited by 4
- DvdNotUnit.not_isUnitproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- DivisorChain.element_of_chain_eq_pow_second_of_chainproof · cited by 1