Theorems · Theorem · group theory
Finset.sum_range_tsub
∀ {M : Type u_4} [inst : AddCommMonoid M] [inst_1 : PartialOrder M] [inst_2 : Sub M] [OrderedSub M] [AddLeftMono M]
[AddLeftReflectLE M] [ExistsAddOfLE M] {f : ℕ → M},
Monotone f → ∀ (n : ℕ), ∑ i ∈ Finset.range n, (f (i + 1) - f i) = f n - f 0A telescoping sum along {0, ..., n-1} of an ℕ-valued function reduces to the difference of
the last and first terms when the function we are summing is monotone.
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 70 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
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
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumstatement · cited by 5,195
- zero_addproof · cited by 2,366
- Monotonestatement and proof · cited by 1,397
- Finset.rangestatement · cited by 1,341
- AddLeftMonostatement and proof · cited by 687
- ExistsAddOfLEstatement and proof · cited by 330
- OrderedSubstatement and proof · cited by 236
- AddLeftReflectLEstatement and proof · cited by 119
- add_tsub_cancel_of_leproof · cited by 79
- tsub_add_eq_add_tsubproof · cited by 23
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