Theorems · Theorem · group theory
Finset.eq_one_of_prod_eq_one
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] {s : Finset ι} {f : ι → M} {a : ι},
∏ x ∈ s, f x = 1 → (∀ x ∈ s, x ≠ a → f x = 1) → ∀ x ∈ s, f x = 1If a product is 1 and the function is 1 except possibly at one
point, it is 1 everywhere on the Finset.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoid
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Cites7
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_singletonproof · cited by 78
- Finset.singleton_subset_iffproof · cited by 38
- Finset.prod_subsetproof · cited by 31
- Finset.notMem_singletonproof · cited by 13
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