Theorems · Theorem · group theory
ne_zero_of_dvd_ne_zero
∀ {α : Type u_1} [inst : MonoidWithZero α] {p q : α}, q ≠ 0 → p ∣ q → p ≠ 0- Cited by
- 26 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- MonoidWithZero
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.
- MonoidWithZerostatement and proof · cited by 456
- left_ne_zero_of_mulproof · cited by 27
Cited by26
Results whose statement or proof uses this declaration.
- WfDvdMonoid.exists_irreducible_factorproof · cited by 12
- WfDvdMonoid.induction_on_irreducibleproof · cited by 5
- Nat.divisors_filter_dvd_of_dvdproof · cited by 4
- DivisorChain.second_of_chain_is_irreducibleproof · cited by 3
- Subgroup.finiteIndex_of_leproof · cited by 3
- IsIntegrallyClosed.eq_map_mul_C_of_dvdproof · cited by 2
- Associates.eq_pow_count_factors_of_dvd_powproof · cited by 2
- map_prime_of_factor_orderIsoproof · cited by 2
- BoundingSieve.nu_inv_eq_sum_divisors_inv_selbergTermsproof · cited by 2
- IsCyclic.normalizer_le_centralizerproof · cited by 2
- DivisorChain.element_of_chain_eq_pow_second_of_chainproof · cited by 1
- ArithmeticFunction.carmichael_dvdproof · cited by 1