Theorems · Theorem · order theory
Finset.add_sum_Ioc_eq_sum_Icc
∀ {α : Type u_1} {M : Type u_2} [inst : AddCommMonoid M] {f : α → M} {a b : α} [inst_1 : PartialOrder α]
[inst_2 : LocallyFiniteOrder α], a ≤ b → f a + ∑ x ∈ Finset.Ioc a b, f x = ∑ x ∈ Finset.Icc a b, f x- Cited by
- 5 results in Mathlib
- Foundations
- Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
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
- PartialOrderstatement and proof · cited by 6,410
- Finset.sumstatement and proof · cited by 5,195
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iccstatement · cited by 348
- Finset.Iocstatement and proof · cited by 301
- Finset.sum_consproof · cited by 84
- Finset.left_notMem_Iocproof · cited by 8
- Finset.Icc_eq_cons_Iocproof · cited by 6
Cited by5
Results whose statement or proof uses this declaration.
- Chebyshev.theta_eq_sum_Iccproof · cited by 3
- Finset.sum_Ioc_add_eq_sum_Iccproof · cited by 2
- sum_mul_eq_sub_integral_mul₁proof · cited by 2
- Chebyshev.psi_eq_theta_add_sum_theta'proof · cited by 1
- Chebyshev.psi_eq_sum_Iccproof · cited by 0