Theorems · Theorem · commutative algebra
EuclideanDomain.lcm_eq_zero_iff
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] {x y : R},
EuclideanDomain.lcm x y = 0 ↔ x = 0 ∨ y = 0- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 0 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.
Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MulZeroClass.mul_zeroproof · cited by 2,091
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_left₀proof · cited by 111
- mul_eq_zeroproof · cited by 94
- EuclideanDomain.gcdproof · cited by 39
- EuclideanDomain.mul_div_assocproof · cited by 8
- EuclideanDomain.lcmstatement and proof · cited by 8
- EuclideanDomain.gcd_dvdproof · cited by 8
- EuclideanDomain.gcd_dvd_rightproof · cited by 6
- EuclideanDomain.gcd_eq_zero_iffproof · cited by 4
- EuclideanDomain.lcm_zero_leftproof · cited by 1
- EuclideanDomain.lcm_zero_rightproof · cited by 1
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