Theorems · Theorem · order theory
Finset.Icc_eq_cons_Ioc
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : LocallyFiniteOrder α] {a b : α},
a ≤ b → Finset.Icc a b = Finset.cons a (Finset.Ioc a b) ⋯Finset.cons version of Finset.Ioc_insert_left.
- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement and proof · cited by 13,712
- PartialOrderstatement and proof · cited by 6,410
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iccstatement and proof · cited by 348
- Finset.Iocstatement and proof · cited by 301
- Finset.consstatement · cited by 221
- Finset.cons_eq_insertproof · cited by 59
- Finset.left_notMem_Iocstatement and proof · cited by 8
- Finset.Ioc_insert_leftproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- Finset.add_sum_Ioc_eq_sum_Iccproof · cited by 5
- Finset.mul_prod_Ioc_eq_prod_Iccproof · cited by 1
- sum_mul_eq_sub_integral_mulproof · cited by 1
- sum_mul_eq_sub_integral_mul₀proof · cited by 1
- Polynomial.coeff_divByMonic_X_sub_Cproof · cited by 0
- summable_mul_of_bigO_atTop'proof · cited by 0