Theorems · Theorem · group theory
Fin.sum_Iic_sub
∀ {M : Type u_3} [inst : AddCommGroup M] {n : ℕ} (a : Fin n) (f : Fin (n + 1) → M),
∑ i ≤ a, (f i.succ - f i.castSucc) = f a.succ - f 0Telescopic sum over Fin.
- Defined in
- Mathlib.Algebra.BigOperators.Intervals
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 80 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.
Cites12
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.Iicstatement and proof · cited by 280
- Finset.mem_rangeproof · cited by 140
- Finset.mem_Iicproof · cited by 42
- Finset.sum_range_subproof · cited by 15
- Order.lt_add_one_iffproof · cited by 13
- Order.add_one_le_iffproof · cited by 8
- Finset.sum_congr_of_eq_on_interproof · cited by 6
- Finset.sum_fin_eq_sum_rangeproof · cited by 6
- Finset.sum_ite_mem_eqproof · cited by 2
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.