Theorems · Theorem · group theory
Set.indicator_singleton
∀ {ι : Type u_6} [inst : DecidableEq ι] {M : Type u_7} [inst_1 : Zero M] (i : ι) (f : ι → M),
{i}.indicator f = Pi.single i (f i)On non-dependent functions, Set.indicator on a singleton set equals Pi.single.
- Defined in
- Mathlib.Algebra.Group.Indicator
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEqZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Set.indicatorstatement · cited by 723
- Pi.singlestatement · cited by 518
- Set.mem_singleton_iffproof · cited by 172
- Pi.single_applyproof · cited by 78
- Set.indicator_applyproof · cited by 48
Cited by6
Results whose statement or proof uses this declaration.
- ProbabilityTheory.setBernoulli_ae_subsetproof · cited by 5
- NNReal.coe_singleproof · cited by 2
- Finsupp.set_indicator_singletonproof · cited by 1
- WeakFEPair.f_modif_aux2proof · cited by 1