Theorems · Theorem · group theory
Finset.sum_Ico_sub
∀ {M : Type u_4} (f : ℕ → M) {m n : ℕ} [inst : AddCommGroup M],
m ≤ n → ∑ i ∈ Finset.Ico m n, (f (i + 1) - f i) = f n - f m- Defined in
- Mathlib.Algebra.BigOperators.Intervals
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- AddCommGroup
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.
- AddCommGroupstatement and proof · cited by 12,871
- Finset.sumstatement and proof · cited by 5,195
- Finset.rangeproof · cited by 1,341
- Finset.Icostatement · cited by 450
- sub_sub_sub_cancel_rightproof · cited by 34
- Finset.sum_range_subproof · cited by 15
- Finset.sum_Ico_eq_subproof · cited by 14
Cited by1
Results whose statement or proof uses this declaration.
- Finset.sum_Icc_subproof · cited by 1