Theorems · Theorem · number theory
Int.sum_modEq_ite
∀ {α : Type u_1} {n : ℤ} {f : α → ℤ} [inst : DecidableEq α] {s : Finset α} {a : α},
(∀ x ∈ s, x ≠ a → f x ≡ 0 [ZMOD n]) → ∑ x ∈ s, f x ≡ if a ∈ s then f a else 0 [ZMOD n]- Defined in
- Mathlib.Algebra.BigOperators.ModEq
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- DecidableEq
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Finset.sumstatement and proof · cited by 5,195
- ZModproof · cited by 1,024
- Int.cast_zeroproof · cited by 188
- Int.ModEqstatement and proof · cited by 147
- Int.cast_sumproof · cited by 9
- Int.modEq_natAbsproof · cited by 5
- Finset.sum_eq_iteproof · cited by 4
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