Theorems · Theorem · group theory
Finset.sum_filter_ne_zero
∀ {ι : Type u_1} {M : Type u_4} [inst : AddCommMonoid M] {f : ι → M} (s : Finset ι)
[inst_1 : (x : ι) → Decidable (f x ≠ 0)], ∑ x ∈ s with f x ≠ 0, f x = ∑ x ∈ s, f x- Cited by
- 14 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidable
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
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Finset.filterstatement · cited by 949
- Finset.sum_filter_of_neproof · cited by 11
Cited by14
Results whose statement or proof uses this declaration.
- Finset.sum_bij_ne_zeroproof · cited by 3
- Multiset.sum_count_eq_cardproof · cited by 3
- ConvexOn.exists_ge_of_centerMassproof · cited by 2
- Real.geom_mean_lt_arith_mean_weighted_iff_of_nonnegproof · cited by 1
- IsVisible.mem_convexHull_isVisibleproof · cited by 1
- SimpleGraph.even_card_odd_degree_verticesproof · cited by 1
- StrictConvexOn.map_sum_eq_iff'proof · cited by 1
- StrictConvexOn.map_sum_eq_iff_of_nonnegproof · cited by 1
- Real.geom_mean_eq_arith_mean_weighted_iff_of_nonnegproof · cited by 1
- Real.geom_mean_eq_arith_mean_weighted_iff_of_nonneg'proof · cited by 1
- StrictConvexOn.map_sum_lt_iff_of_nonneg'proof · cited by 1
- eq_pos_convex_span_of_mem_convexHullproof · cited by 0