Theorems · Theorem · group theory
Finset.exists_ne_one_of_prod_ne_one
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : CommMonoid M] {f : ι → M}, ∏ x ∈ s, f x ≠ 1 → ∃ a ∈ s, f a ≠ 1- Cited by
- 1 results in Mathlib
- Foundations
- Depth 57 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
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.
- Finsetstatement and proof · cited by 13,712
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.prod_eq_oneproof · cited by 22
Cited by1
Results whose statement or proof uses this declaration.
- finprod_prod_filterproof · cited by 0