Theorems · Theorem · group theory
Finset.sum_range_one
∀ {M : Type u_4} [inst : AddCommMonoid M] (f : ℕ → M), ∑ k ∈ Finset.range 1, f k = f 0- Cited by
- 13 results in Mathlib
- Foundations
- Depth 55 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.
- Finsetproof · cited by 13,712
- AddCommMonoidstatement and proof · cited by 12,281
- Finset.sumstatement and proof · cited by 5,195
- Finset.rangestatement · cited by 1,341
- Finset.sum_singletonproof · cited by 251
- Finset.range_oneproof · cited by 7
Cited by13
Results whose statement or proof uses this declaration.
- eVariationOn.edist_leproof · cited by 7
- Finset.sum_flipproof · cited by 4
- HasFPowerSeriesWithinOnBall.isBigO_image_sub_image_sub_deriv_principalproof · cited by 3
- tsum_eq_zero_add'proof · cited by 3
- HasSum.zero_addproof · cited by 3
- HasSum.of_nat_of_negproof · cited by 2
- HurwitzZeta.hasSum_nat_cosKernel₀proof · cited by 1
- hasSum_nat_jacobiThetaproof · cited by 1
- birkhoffSum_oneproof · cited by 1
- PadicInt.addChar_of_value_at_one_defproof · cited by 1
- Polynomial.Monic.not_irreducible_iff_exists_add_mul_eq_coeffproof · cited by 1
- Polynomial.sumIDeriv_Cproof · cited by 0