Theorems · Theorem · commutative algebra
EuclideanDomain.dvd_lcm_left
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] (x y : R), x ∣ EuclideanDomain.lcm x y- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 24 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.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- mul_assocproof · cited by 1,667
- EuclideanDomainstatement and proof · cited by 124
- mul_right_commproof · cited by 108
- dvd_zeroproof · cited by 63
- EuclideanDomain.gcdproof · cited by 39
- by_casesproof · cited by 31
- EuclideanDomain.div_zeroproof · cited by 17
- EuclideanDomain.lcmstatement and proof · cited by 8
- EuclideanDomain.gcd_dvdproof · cited by 8
- EuclideanDomain.eq_div_of_mul_eq_leftproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- EuclideanDomain.lcm_dvd_iffproof · cited by 0