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Theorems · Theorem · commutative algebra

EuclideanDomain.dvd_gcd

∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] {a b c : R},
  c ∣ a → c ∣ b → c ∣ EuclideanDomain.gcd a b
Defined in
Mathlib.Algebra.EuclideanDomain.Basic
Cited by
1 results in Mathlib
Foundations
Depth 23 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.

Int.natAbs_euclideanDomain_gcd · cited by 0Int.natAbs_euclideanDomai…EuclideanDomain.gcdMonoid · cited by 0EuclideanDomain.gcdMonoidEuclideanDomain · cited by 124EuclideanDomainEuclideanDomain.gcd · cited by 39EuclideanDomain.gcdEuclideanDomain.gcd_zero_left · cited by 7EuclideanDomain.gcd_zero_…EuclideanDomain.gcd_val · cited by 5EuclideanDomain.gcd_valEuclideanDomain.GCD.induction · cited by 5GCD.inductionEuclideanDomain.dvd_mod_iff · cited by 2EuclideanDomain.dvd_mod_i…EuclideanDomain.dvd_gcdCITED BYCITES

Cites6

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Cited by2

Results whose statement or proof uses this declaration.