Theorems · Definition · commutative algebra
EuclideanDomain.r
{R : Type u} → [self : EuclideanDomain R] → R → R → PropA well-founded relation on R, satisfying r (a % b) b.
This ensures that the GCD algorithm always terminates.
- Defined in
- Mathlib.Algebra.EuclideanDomain.Defs
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 1 from the axioms · uses no axioms
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- EuclideanDomainstatement and proof · cited by 124
Cited by17
Results whose statement or proof uses this declaration.
- EuclideanDomain.mod_ltstatement · cited by 8
- EuclideanDomain.gcd_valproof · cited by 5
- EuclideanDomain.mul_left_not_ltstatement · cited by 3
- EuclideanDomain.xgcdAux_recproof · cited by 2
- EuclideanDomain.remainder_ltstatement · cited by 2
- AbsoluteValue.IsEuclidean.map_lt_map_iff'statement · cited by 1
- EuclideanDomain.gcd.eq_defstatement · cited by 1
- EuclideanDomain.xgcdAux.eq_defstatement · cited by 1
- AbsoluteValue.IsEuclidean.map_lt_map_iffstatement · cited by 1
- AbsoluteValue.IsEuclidean.recOnstatement and proof · cited by 0
- RingEquiv.euclideanDomainproof · cited by 0
- EuclideanDomain.lt_onestatement and proof · cited by 0