Theorems · Theorem · group theory
exists_dvd_and_dvd_of_dvd_mul
∀ {α : Type u_1} [inst : Semigroup α] [DecompositionMonoid α] {b c a : α},
a ∣ b * c → ∃ a₁ a₂, a₁ ∣ b ∧ a₂ ∣ c ∧ a = a₁ * a₂- Defined in
- Mathlib.Algebra.Divisibility.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- SemigroupDecompositionMonoid
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.
- Semigroupstatement and proof · cited by 202
- DecompositionMonoidstatement and proof · cited by 39
- DecompositionMonoid.primalproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Squarefree.isRadicalproof · cited by 7
- IsRelPrime.mul_leftproof · cited by 3
- exists_associated_pow_of_mul_eq_powproof · cited by 3
- gcd_mul_dvd_mul_gcdproof · cited by 2
- Squarefree.dvd_of_squarefree_of_mul_dvd_mul_rightproof · cited by 2
- dvd_mulproof · cited by 0