Theorems · Theorem · commutative algebra
Ideal.single_mem_pi
∀ {ι : Type u_1} {R : ι → Type u_5} [inst : (i : ι) → Semiring (R i)] {I : (i : ι) → Ideal (R i)}
[inst_1 : DecidableEq ι] {i : ι} {r : R i}, r ∈ I i → Pi.single i r ∈ Ideal.pi I- Defined in
- Mathlib.RingTheory.Ideal.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 18 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SemiringDecidableEq
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.
- Semiringstatement and proof · cited by 13,802
- Idealstatement and proof · cited by 4,748
- eq_or_neproof · cited by 1,117
- Pi.singlestatement · cited by 518
- Pi.single_eq_sameproof · cited by 144
- Pi.single_eq_of_ne'proof · cited by 33
- Ideal.pistatement · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.map_evalRingHom_piproof · cited by 0
- Ideal.pi_le_pi_iffproof · cited by 0