Theorems · Theorem · number theory
IsRelPrime.dvd_of_dvd_mul_right
∀ {α : Type u_1} [inst : CommMonoid α] {x y z : α} [DecompositionMonoid α], IsRelPrime x z → x ∣ y * z → x ∣ y- Defined in
- Mathlib.Algebra.Divisibility.Units
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommMonoidstatement and proof · cited by 2,264
- IsRelPrimestatement and proof · cited by 136
- DecompositionMonoidstatement and proof · cited by 39
- DecompositionMonoid.primalproof · cited by 5
- IsRelPrime.dvd_of_dvd_mul_right_of_isPrimalproof · cited by 2
Cited by4
Results whose statement or proof uses this declaration.
- UniqueFactorizationMonoid.dvd_of_dvd_mul_left_of_no_prime_factorsproof · cited by 3
- IsRelPrime.dvd_of_dvd_mul_leftproof · cited by 1
- IsFractionRing.num_den_uniqueproof · cited by 1
- IsFractionRing.associated_den_num_invproof · cited by 1