Theorems · Theorem · order theory
Finset.sum_eq_sum_Ico_succ_bot
∀ {M : Type u_2} [inst : AddCommMonoid M] {a b : ℕ},
a < b → ∀ (f : ℕ → M), ∑ k ∈ Finset.Ico a b, f k = f a + ∑ k ∈ Finset.Ico (a + 1) b, f k- Cited by
- 8 results in Mathlib
- Foundations
- Depth 63 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.
Cites10
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
- one_ne_zeroproof · cited by 885
- Finset.Icostatement and proof · cited by 450
- Finset.sum_insertproof · cited by 196
- nonpos_iff_eq_zeroproof · cited by 100
- Finset.mem_Icoproof · cited by 50
- add_le_iff_nonpos_rightproof · cited by 9
- Finset.insert_Ico_add_one_left_eq_Icoproof · cited by 4
Cited by8
Results whose statement or proof uses this declaration.
- Finset.sum_range_eq_add_Icoproof · cited by 2
- HasFPowerSeriesWithinAt.compproof · cited by 2
- Finset.sum_Ico_by_partsproof · cited by 2
- Finset.sum_Ico_sub_botproof · cited by 1
- sum_Ioo_inv_sq_leproof · cited by 1
- eVariationOn.add_pointproof · cited by 1
- HasFPowerSeriesAt.tendsto_partialSum_prod_of_compproof · cited by 1
- Nat.sum_totient'proof · cited by 0