Theorems · Theorem · group theory
Finset.prod_filter_of_ne
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : CommMonoid M] {f : ι → M} {p : ι → Prop}
[inst_1 : DecidablePred p], (∀ x ∈ s, f x ≠ 1 → p x) → ∏ x ∈ s with p x, f x = ∏ x ∈ s, f x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidDecidablePred
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.
- 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.mem_filterproof · cited by 185
- not_imp_commproof · cited by 56
- Finset.filter_subsetproof · cited by 55
- Finset.prod_subsetproof · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- Finset.prod_preimageproof · cited by 4
- Finset.prod_filter_ne_oneproof · cited by 2
- centralBinom_le_of_no_bertrand_primeproof · cited by 1