Theorems · Theorem · combinatorics
Finset.sum_fin_eq_sum_range
∀ {β : Type u_2} [inst : AddCommMonoid β] {n : ℕ} (c : Fin n → β),
∑ i, c i = ∑ i ∈ Finset.range n, if h : i < n then c ⟨i, h⟩ else 0- Defined in
- Mathlib.Data.Fintype.BigOperators
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommMonoid
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.
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- Finset.sum_congrproof · cited by 2,323
- Finset.rangestatement · cited by 1,341
- Fin.sum_univ_eq_sum_rangeproof · cited by 10
Cited by6
Results whose statement or proof uses this declaration.
- Real.fibRec_charPoly_eqproof · cited by 2
- Real.fib_isSol_fibRecproof · cited by 1
- Finset.sum_fin_Icc_eq_sum_nat_Iccproof · cited by 1
- Polynomial.discr_of_degree_eq_threeproof · cited by 0
- Matrix.two_mul_explproof · cited by 0
- Fin.sum_Iic_subproof · cited by 0