Theorems · Theorem · group theory
Finset.sum_ite_of_false
∀ {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, g x- Cited by
- 6 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_falseproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- DirectSum.coe_of_mul_apply_of_not_leproof · cited by 2
- RootPairing.GeckConstruction.isNilpotent_eproof · cited by 2
- DirectSum.coe_mul_of_apply_of_not_leproof · cited by 2
- QuadraticMap.toQuadraticMap_toBilinproof · cited by 1
- RootPairing.GeckConstruction.lie_e_f_neproof · cited by 0
- Finset.sum_apply_ite_of_falseproof · cited by 0