Theorems · Theorem · commutative algebra
mod_mem_iff
∀ {R : Type u} [inst : EuclideanDomain R] {S : Ideal R} {x y : R}, y ∈ S → (x % y ∈ S ↔ x ∈ S)- Defined in
- Mathlib.RingTheory.PrincipalIdealDomain
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext
- Assumes
- EuclideanDomain
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Idealstatement and proof · cited by 4,748
- EuclideanDomainstatement and proof · cited by 124
- Ideal.mul_mem_rightproof · cited by 71
- Ideal.add_memproof · cited by 36
- Ideal.sub_memproof · cited by 22
- EuclideanDomain.div_add_modproof · cited by 10
- EuclideanDomain.mod_eq_sub_mul_divproof · cited by 2
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