Theorems · Theorem · group theory
Finset.sum_flip
∀ {M : Type u_4} [inst : AddCommMonoid M] {n : ℕ} (f : ℕ → M),
∑ r ∈ Finset.range (n + 1), f (n - r) = ∑ k ∈ Finset.range (n + 1), f k- Cited by
- 4 results in Mathlib
- Foundations
- Depth 71 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.
Cites7
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.sum_congrproof · cited by 2,323
- Finset.rangestatement and proof · cited by 1,341
- Finset.sum_range_succproof · cited by 121
- Finset.sum_range_succ'proof · cited by 37
- Finset.sum_range_oneproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- Finset.lubell_yamamoto_meshalkin_inequality_sum_card_div_chooseproof · cited by 2
- Commute.geom_sum₂_commproof · cited by 1
- Polynomial.sum_range_pow_eq_bernoulli_subproof · cited by 1
- Nat.sum_range_mul_chooseproof · cited by 0