Theorems · Theorem · group theory
Finset.sum_ite_of_true
∀ {ι : Type u_1} {M : Type u_3} {s : Finset ι} [inst : AddCommMonoid M] {p : ι → Prop} [inst_1 : DecidablePred p],
(∀ x ∈ s, p x) → ∀ (f g : ι → M), (∑ x ∈ s, if p x then f x else g x) = ∑ x ∈ s, f x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 78 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.
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.sum_attachproof · cited by 54
- Finset.sum_dite_of_trueproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- convexHull_range_eq_exists_affineCombinationproof · cited by 2
- OrthogonalFamily.inner_sumproof · cited by 1
- Finset.sum_apply_ite_of_trueproof · cited by 0