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Theorems · Theorem · commutative algebra

EuclideanDomain.gcd_eq_zero_iff

∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] {a b : R},
  EuclideanDomain.gcd a b = 0 ↔ a = 0 ∧ b = 0
Defined in
Mathlib.Algebra.EuclideanDomain.Basic
Cited by
4 results in Mathlib
Foundations
Depth 24 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
EuclideanDomainDecidableEq
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Around this declaration

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

Field.primitive_element_inf_aux · cited by 1Field.primitive_element_i…EuclideanDomain.lcm_dvd · cited by 1EuclideanDomain.lcm_dvdEuclideanDomain.lcm_eq_zero_iff · cited by 0EuclideanDomain.lcm_eq_ze…EuclideanDomain.gcd_mul_lcm · cited by 0EuclideanDomain.gcd_mul_l…EuclideanDomain · cited by 124EuclideanDomainEuclideanDomain.gcd · cited by 39EuclideanDomain.gcdEuclideanDomain.gcd_dvd · cited by 8EuclideanDomain.gcd_dvdEuclideanDomain.gcd_zero_right · cited by 2EuclideanDomain.gcd_zero_…EuclideanDomain.gcd_eq_zero_i…CITED BYCITES

Cites4

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Cited by4

Results whose statement or proof uses this declaration.