Theorems · Theorem · commutative algebra
EuclideanDomain.lcm_dvd
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] {x y z : R},
x ∣ z → y ∣ z → EuclideanDomain.lcm x y ∣ z- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 51 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EuclideanDomainDecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_commproof · cited by 2,262
- mul_assocproof · cited by 1,667
- mul_addproof · cited by 413
- mul_left_commproof · cited by 184
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_left₀proof · cited by 111
- mul_right_commproof · cited by 108
- EuclideanDomain.gcdproof · cited by 39
- mul_left_inj'proof · cited by 35
- mul_dvd_mul_leftproof · cited by 34
- dvd_addproof · cited by 25
- EuclideanDomain.div_zeroproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanDomain.lcm_dvd_iffproof · cited by 0