Theorems · Theorem · commutative algebra
EuclideanDomain.gcd_val
∀ {R : Type u} [inst : EuclideanDomain R] [inst_1 : DecidableEq R] (a b : R),
EuclideanDomain.gcd a b = EuclideanDomain.gcd (b % a) a- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 22 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.rproof · cited by 13
- EuclideanDomain.mod_ltproof · cited by 8
- EuclideanDomain.mod_zeroproof · cited by 4
- EuclideanDomain.gcd_zero_rightproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- EuclideanDomain.gcd_dvdproof · cited by 8
- EuclideanDomain.gcd_eq_leftproof · cited by 2
- Polynomial.gcd_mapproof · cited by 2
- EuclideanDomain.dvd_gcdproof · cited by 1
- EuclideanDomain.xgcdAux_fstproof · cited by 1