Theorems · Theorem · group theory
Set.indicator_self_add_compl_apply
∀ {α : Type u_1} {M : Type u_4} [inst : AddZeroClass M] (s : Set α) (f : α → M) (a : α),
s.indicator f a + sᶜ.indicator f a = f a- Defined in
- Mathlib.Algebra.Group.Indicator
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 15 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddZeroClass
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- Compl.complstatement · cited by 2,925
- add_zeroproof · cited by 2,707
- zero_addproof · cited by 2,366
- AddZeroClassstatement and proof · cited by 1,237
- Set.indicatorstatement · cited by 723
- Set.indicator_of_memproof · cited by 161
- Set.indicator_of_notMemproof · cited by 154
- Set.mem_compl_iffproof · cited by 53
- by_casesproof · cited by 31
Cited by3
Results whose statement or proof uses this declaration.
- HasSum.add_isComplproof · cited by 4
- Set.indicator_self_add_complproof · cited by 2
- ENNReal.sum_add_tsum_complproof · cited by 0