Theorems · Theorem · ring theory
List.prod_ne_zero
∀ {M₀ : Type u_4} [inst : MonoidWithZero M₀] {l : List M₀} [Nontrivial M₀] [NoZeroDivisors M₀], 0 ∉ l → l.prod ≠ 0- Defined in
- Mathlib.Algebra.BigOperators.Ring.List
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext
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.
- Nontrivialstatement and proof · cited by 2,416
- NoZeroDivisorsstatement and proof · cited by 545
- MonoidWithZerostatement and proof · cited by 456
- List.prod_eq_zero_iffproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- jacobiSym.list_prod_rightproof · cited by 1
- Polynomial.roots_list_prodproof · cited by 1
- Nat.prod_mem_factoredNumbersproof · cited by 0