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Theorems · Theorem · number theory

IsRelPrime.mul_dvd

∀ {α : Type u_1} [inst : CommMonoid α] {x y z : α} [DecompositionMonoid α], IsRelPrime x y → x ∣ z → y ∣ z → x * y ∣ z
Defined in
Mathlib.Algebra.Divisibility.Units
Cited by
2 results in Mathlib
Foundations
Depth 15 from the axioms · uses no axioms
Assumes
CommMonoidDecompositionMonoid
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Squarefree.isRadical · cited by 7Squarefree.isRadicalFinset.prod_dvd_of_isRelPrime · cited by 3Finset.prod_dvd_of_isRelP…CommMonoid · cited by 2264CommMonoidIsRelPrime · cited by 136IsRelPrimeDecompositionMonoid · cited by 39DecompositionMonoidDecompositionMonoid.primal · cited by 5DecompositionMonoid.primalIsRelPrime.mul_dvd_of_left_isPrimal · cited by 1IsRelPrime.mul_dvd_of_lef…IsRelPrime.mul_dvdCITED BYCITES

Cites5

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Cited by2

Results whose statement or proof uses this declaration.