Theorems · Theorem · commutative algebra
prod_mem_nonZeroDivisors_of_mem_nonZeroDivisors
∀ {M₀ : Type u_1} [inst : CommMonoidWithZero M₀] {ι : Type u_2} {s : Finset ι} {f : ι → M₀},
(∀ i ∈ s, f i ∈ nonZeroDivisors M₀) → ∏ i ∈ s, f i ∈ nonZeroDivisors M₀- Cited by
- 1 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
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.
- Finsetstatement and proof · cited by 13,712
- Submonoidstatement · cited by 3,086
- Finset.prodstatement · cited by 2,356
- CommMonoidWithZerostatement and proof · cited by 913
- nonZeroDivisorsstatement and proof · cited by 895
- OneMemClass.one_memproof · cited by 87
- Finset.prod_inductionproof · cited by 18
- mul_mem_nonZeroDivisorsproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_prod_of_mem_nonZeroDivisorsproof · cited by 1