Theorems · Theorem · commutative algebra
EuclideanDomain.dvd_mod_iff
∀ {R : Type u} [inst : EuclideanDomain R] {a b c : R}, c ∣ b → (c ∣ a % b ↔ c ∣ a)- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses propext, Quot.sound
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- EuclideanDomainstatement and proof · cited by 124
- Dvd.dvd.mul_rightproof · cited by 15
- EuclideanDomain.div_add_modproof · cited by 10
- dvd_add_rightproof · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- EuclideanDomain.gcd_dvdproof · cited by 8
- EuclideanDomain.dvd_gcdproof · cited by 1