Theorems · Theorem · group theory
AddChar.sum_eq_ite
∀ {A : Type u_1} {R : Type u_2} [inst : AddGroup A] [inst_1 : Fintype A] [inst_2 : CommSemiring R] [IsDomain R]
(ψ : AddChar A R) [inst_4 : Decidable (ψ = 0)], ∑ a, ψ a = if ψ = 0 then ↑(Fintype.card A) else 0- Defined in
- Mathlib.Algebra.Group.AddChar
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommSemiringstatement and proof · cited by 10,911
- Fintypestatement and proof · cited by 7,736
- Finset.sumstatement and proof · cited by 5,195
- AddGroupstatement and proof · cited by 4,410
- mul_oneproof · cited by 3,885
- Finset.univstatement and proof · cited by 3,473
- IsDomainstatement and proof · cited by 2,196
- Fintype.cardstatement and proof · cited by 1,386
- nsmul_eq_mulproof · cited by 369
- AddCharstatement and proof · cited by 286
- Finset.sum_constproof · cited by 254
Cited by3
Results whose statement or proof uses this declaration.
- AddChar.expect_eq_iteproof · cited by 2
- AddChar.sum_eq_zero_iff_ne_zeroproof · cited by 1
- AddChar.sum_apply_eq_iteproof · cited by 1