Theorems · Theorem · combinatorics
Fin.sum_univ_eq_sum_range
∀ {α : Type u_1} [inst : AddCommMonoid α] (f : ℕ → α) (n : ℕ), ∑ i, f ↑i = ∑ i ∈ Finset.range n, f iIt is equivalent to sum a function over fin n or finset.range n.
- Defined in
- Mathlib.Data.Fintype.BigOperators
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 78 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.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement · cited by 3,473
- Finset.rangestatement and proof · cited by 1,341
- Equiv.transproof · cited by 337
- Finset.mem_rangeproof · cited by 140
- Finset.sum_attachproof · cited by 54
- Fintype.sum_equivproof · cited by 35
- Equiv.subtypeEquivRightproof · cited by 17
- Finset.attach_eq_univproof · cited by 9
Cited by10
Results whose statement or proof uses this declaration.
- Finset.sum_rangeproof · cited by 18
- xInTermsOfW_eqproof · cited by 7
- bernoulli'_defproof · cited by 7
- Finset.sum_fin_eq_sum_rangeproof · cited by 6
- minpoly_algEquiv_toLinearMapproof · cited by 2
- Polynomial.sum_finproof · cited by 2
- WittVector.frobeniusPolyAux_eqproof · cited by 1
- Matrix.eval_matrixOfPolynomials_eq_vandermonde_mul_matrixOfPolynomialsproof · cited by 1
- FiniteField.algebraMap_norm_eq_powproof · cited by 1
- SimpleGraph.card_edgeFinset_turanGraph_addproof · cited by 0