Theorems · Theorem · commutative algebra
EuclideanDomain.mod_eq_zero
∀ {R : Type u} [inst : EuclideanDomain R] {a b : R}, a % b = 0 ↔ b ∣ a- Defined in
- Mathlib.Algebra.EuclideanDomain.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- add_zeroproof · cited by 2,707
- MulZeroClass.zero_mulproof · cited by 1,625
- EuclideanDomainstatement and proof · cited by 124
- mul_div_cancel_left₀proof · cited by 111
- dvd_mul_rightproof · cited by 89
- add_left_cancel_iffproof · cited by 17
- EuclideanDomain.div_add_modproof · cited by 10
- Classical.decproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- EuclideanDomain.gcd_eq_leftproof · cited by 2
- EuclideanDomain.zero_modproof · cited by 1
- EuclideanDomain.mod_oneproof · cited by 0
- EuclideanDomain.mod_selfproof · cited by 0