Theorems · Theorem · commutative algebra
Prime.dvd_or_dvd
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {p : M}, Prime p → ∀ {a b : M}, p ∣ a * b → p ∣ a ∨ p ∣ b- Defined in
- Mathlib.Algebra.Prime.Defs
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidWithZerostatement and proof · cited by 913
- Primestatement and proof · cited by 277
Cited by17
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- Ideal.isPrime_of_primeproof · cited by 17
- Prime.dvd_of_dvd_powproof · cited by 14
- Associated.primeproof · cited by 4
- Prime.dvd_mulproof · cited by 4
- Prime.dvd_of_pow_dvd_pow_mul_pow_of_square_not_dvdproof · cited by 2
- Prime.dvd_prod_iffproof · cited by 2
- Prime.exists_mem_multiset_dvdproof · cited by 2
- Prime.pow_dvd_of_dvd_mul_leftproof · cited by 2
- Submonoid.LocalizationMap.map_primeproof · cited by 1
- exists_associated_mem_of_dvd_prodproof · cited by 1
- succ_dvd_or_succ_dvd_of_succ_sum_dvd_mulproof · cited by 1