Theorems · Theorem · group theory
dvd_mul_of_dvd_right
∀ {α : Type u_1} [inst : CommSemigroup α] {a b : α}, a ∣ b → ∀ (c : α), a ∣ c * b- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 29 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- CommSemigroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- CommSemigroupstatement and proof · cited by 62
- Dvd.dvd.mul_rightproof · cited by 15
Cited by29
Results whose statement or proof uses this declaration.
- Prime.irreducibleproof · cited by 54
- Dvd.dvd.mul_leftproof · cited by 14
- Prime.dvd_mulproof · cited by 4
- Finsupp.prod_dvd_prod_of_subset_of_dvdproof · cited by 4
- Squarefree.of_mul_rightproof · cited by 3
- X_pow_sub_C_irreducible_of_oddproof · cited by 3
- Rat.add_den_dvd_lcmproof · cited by 3
- den_dvd_of_is_rootproof · cited by 2
- Ideal.exists_isMaximal_dvd_of_dvd_absNormproof · cited by 2
- ZMod.isSquare_neg_one_iff_forall_mem_primeFactors_mod_four_ne_threeproof · cited by 2
- exists_eq_pow_of_mul_eq_pow_of_coprimeproof · cited by 1
- divRadical_dvd_derivativeproof · cited by 1