Theorems · Theorem · order theory
Finset.mul_prod_Ioc_eq_prod_Icc
∀ {α : Type u_1} {M : Type u_2} [inst : CommMonoid 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
- 1 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
- PartialOrderstatement and proof · cited by 6,410
- Finset.prodstatement and proof · cited by 2,356
- CommMonoidstatement and proof · cited by 2,264
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iccstatement · cited by 348
- Finset.Iocstatement and proof · cited by 301
- Finset.prod_consproof · cited by 60
- Finset.left_notMem_Iocproof · cited by 8
- Finset.Icc_eq_cons_Iocproof · cited by 6
Cited by1
Results whose statement or proof uses this declaration.
- Finset.prod_Ioc_mul_eq_prod_Iccproof · cited by 0