Theorems · Theorem · group theory
Finset.sum_filter
∀ {ι : Type u_1} {M : Type u_4} {s : Finset ι} [inst : AddCommMonoid 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 0- Cited by
- 37 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoidDecidablePred
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
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement · cited by 5,195
- Finset.sum_congrproof · cited by 2,323
- Finset.filterstatement and proof · cited by 949
- Finset.mem_filterproof · cited by 185
- Finset.sum_subsetproof · cited by 79
- Finset.filter_subsetproof · cited by 55
Cited by37
Results whose statement or proof uses this declaration.
- ZMod.card_units_eq_totientproof · cited by 15
- Finset.sum_ite_memproof · cited by 14
- AddMonoidAlgebra.coeff_mul_antidiagproof · cited by 3
- Algebra.Generators.map_toComp_kerproof · cited by 3
- Chebyshev.theta_eq_sum_Iccproof · cited by 3
- Matrix.charpoly_sub_diagonal_degree_ltproof · cited by 3
- Fintype.sum_extend_by_zeroproof · cited by 2
- BoundingSieve.nu_inv_eq_sum_divisors_inv_selbergTermsproof · cited by 2
- Finset.sum_card_inter_leproof · cited by 2
- Chebyshev.primeCounting_eq_theta_div_log_add_integralproof · cited by 2
- Finset.sum_ite_mem_eqproof · cited by 2
- FirstOrder.Ring.lift_genericPolyMapproof · cited by 2