Theorems · Theorem · group theory

Finset.sum_dite_of_true

∀ {ι : Type u_1} {M : Type u_3} {s : Finset ι} [inst : AddCommMonoid M] {p : ι → Prop} [inst_1 : DecidablePred p]
  (h : ∀ i ∈ s, p i) (f : (i : ι) → p i → M) (g : (i : ι) → ¬p i → M),
  (∑ i ∈ s, if hi : p i then f i hi else g i hi) = ∑ i, f ↑i ⋯

Defined in: Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
Cited by: 3 results in Mathlib
Foundations: Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: AddCommMonoid DecidablePred

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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.univstatement and proof · cited by 3,473
Finset.sum_bij'proof · cited by 11

Cited by3

Results whose statement or proof uses this declaration.

Finset.sum_ite_of_trueproof · cited by 3
exists_nontrivial_relation_sum_zero_of_not_affine_indproof · cited by 1
Finset.mem_piAntidiagproof · cited by 1