Theorems · Theorem · commutative algebra
EuclideanDomain.lcm_dvd_iff
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] {x y z : R},
EuclideanDomain.lcm x y ∣ z ↔ x ∣ z ∧ y ∣ z- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 52 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Dvd.dvd.transproof · cited by 148
- EuclideanDomainstatement and proof · cited by 124
- EuclideanDomain.lcmstatement and proof · cited by 8
- EuclideanDomain.dvd_lcm_leftproof · cited by 1
- EuclideanDomain.dvd_lcm_rightproof · cited by 1
- EuclideanDomain.lcm_dvdproof · cited by 1
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