Theorems · Theorem · ring theory
TwoSidedIdeal.listProd_mem
∀ {R : Type u_1} [inst : Ring R] (I : TwoSidedIdeal R) {ι : Type u_2} (l : List ι) (f : ι → R),
(∃ x ∈ l, f x ∈ I) → (List.map f l).prod ∈ I- Cited by
- 1 results in Mathlib
- Foundations
- Depth 42 from the axioms · uses propext, Quot.sound
- Assumes
- Ring
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.
- Ringstatement and proof · cited by 7,463
- TwoSidedIdealstatement and proof · cited by 151
- TwoSidedIdeal.mul_mem_leftproof · cited by 8
- TwoSidedIdeal.mul_mem_rightproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- TwoSidedIdeal.multiSetProd_memproof · cited by 1