Theorems · Theorem · commutative algebra
EuclideanDomain.mod_lt
∀ {R : Type u} [inst : EuclideanDomain R] (a : R) {b : R}, b ≠ 0 → EuclideanDomain.r (a % b) b- Defined in
- Mathlib.Algebra.EuclideanDomain.Defs
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 12 from the axioms · uses no axioms
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites3
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.rstatement · cited by 13
- EuclideanDomain.remainder_ltproof · cited by 2
Cited by8
Results whose statement or proof uses this declaration.
- EuclideanDomain.gcd_valproof · cited by 5
- EuclideanDomain.xgcdAux_recproof · cited by 2
- EuclideanDomain.gcd.eq_defstatement · cited by 1
- EuclideanDomain.xgcdAux.eq_defstatement · cited by 1
- Polynomial.exists_approx_polynomialproof · cited by 1
- Polynomial.mod_eq_self_iffproof · cited by 1
- AbsoluteValue.IsEuclidean.sub_mod_ltproof · cited by 0
- Polynomial.degree_add_divproof · cited by 0