Theorems · Theorem · group theory
Finset.prod_filter
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : CommMonoid M] (p : ι → Prop) [inst_1 : DecidablePred p]
(f : ι → M), ∏ a ∈ s with p a, f a = ∏ a ∈ s, if p a then f a else 1- Cited by
- 4 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 and proof · cited by 949
- Finset.prod_congrproof · cited by 646
- Finset.mem_filterproof · cited by 185
- Finset.filter_subsetproof · cited by 55
- Finset.prod_subsetproof · cited by 31
Cited by4
Results whose statement or proof uses this declaration.
- Finset.prod_ite_memproof · cited by 8
- Finset.prod_ite_mem_eqproof · cited by 3
- Finset.prod_prod_bipartiteAbove_eq_prod_prod_bipartiteBelowproof · cited by 0
- Fintype.prod_extend_by_oneproof · cited by 0