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Theorems · Theorem · commutative algebra

EuclideanDomain.gcd_zero_left

∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] (a : R), EuclideanDomain.gcd 0 a = a
Defined in
Mathlib.Algebra.EuclideanDomain.Defs
Cited by
7 results in Mathlib
Foundations
Depth 17 from the axioms · uses Quot.sound
Assumes
EuclideanDomainDecidableEq
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Around this declaration

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

EuclideanDomain.gcd_dvd · cited by 8EuclideanDomain.gcd_dvdEuclideanDomain.gcd_eq_left · cited by 2EuclideanDomain.gcd_eq_le…Field.gcd_eq · cited by 2Field.gcd_eqEuclideanDomain.gcd_zero_right · cited by 2EuclideanDomain.gcd_zero_…Polynomial.gcd_map · cited by 2Polynomial.gcd_mapEuclideanDomain.dvd_gcd · cited by 1EuclideanDomain.dvd_gcdEuclideanDomain.xgcdAux_fst · cited by 1EuclideanDomain.xgcdAux_f…EuclideanDomain · cited by 124EuclideanDomainEuclideanDomain.gcd · cited by 39EuclideanDomain.gcdEuclideanDomain.gcd_zero_leftCITED BYCITES

Cites2

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by7

Results whose statement or proof uses this declaration.