Theorems · Theorem · commutative algebra
EuclideanDomain.gcd_eq_left
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] {a b : R}, EuclideanDomain.gcd a b = a ↔ a ∣ b- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 25 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- EuclideanDomainstatement and proof · cited by 124
- EuclideanDomain.gcdstatement and proof · cited by 39
- EuclideanDomain.gcd_zero_leftproof · cited by 7
- EuclideanDomain.gcd_dvd_rightproof · cited by 6
- EuclideanDomain.gcd_valproof · cited by 5
- EuclideanDomain.mod_eq_zeroproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanDomain.gcd_selfproof · cited by 0
- EuclideanDomain.gcd_one_leftproof · cited by 0