Theorems · Theorem · group theory
finprod_apply_ne_zero
∀ {ι : Type u_7} {N₀ : Type u_8} {M₀ : Type u_9} [inst : CommMonoidWithZero M₀] [Nontrivial M₀] [NoZeroDivisors M₀]
{n : N₀} {f : ι → N₀ → M₀}, (∀ (i : ι), f i n ≠ 0) → (∏ᶠ (i : ι), f i) n ≠ 0- Defined in
- Mathlib.Algebra.BigOperators.Finprod
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- Nontrivialstatement and proof · cited by 2,416
- Set.Finiteproof · cited by 1,814
- CommMonoidWithZerostatement and proof · cited by 913
- NoZeroDivisorsstatement and proof · cited by 545
- finprodstatement · cited by 257
- Function.mulSupportproof · cited by 240
- finprod_of_infinite_mulSupportproof · cited by 13
- finprod_eq_prodproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- Complex.CanonicalDecomp.divisor_eq_divisorproof · cited by 1