Theorems · Theorem · group theory
Finset.prod_filter_ne_one
∀ {ι : Type u_1} {M : Type u_4} [inst : CommMonoid M] {f : ι → M} (s : Finset ι)
[inst_1 : (x : ι) → Decidable (f x ≠ 1)], ∏ x ∈ s with f x ≠ 1, f x = ∏ x ∈ s, f x- Cited by
- 2 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidDecidable
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
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 · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- Finset.filterstatement · cited by 949
- Finset.prod_filter_of_neproof · cited by 3
Cited by2
Results whose statement or proof uses this declaration.
- Finset.prod_biUnion_of_pairwise_eq_oneproof · cited by 0
- Finset.prod_bij_ne_oneproof · cited by 0