Theorems · Theorem · order theory
Finset.Ioc_eq_cons_Ioo
∀ {α : Type u_2} [inst : PartialOrder α] [inst_1 : LocallyFiniteOrder α] {a b : α},
a < b → Finset.Ioc a b = Finset.cons b (Finset.Ioo a b) ⋯Finset.cons version of Finset.Ioo_insert_right.
- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 2 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.Iocstatement and proof · cited by 301
- Finset.consstatement · cited by 221
- Finset.Ioostatement and proof · cited by 185
- Finset.cons_eq_insertproof · cited by 59
- Finset.right_notMem_Ioostatement and proof · cited by 4
- Finset.Ioo_insert_rightproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- Finset.add_sum_Ioo_eq_sum_Iocproof · cited by 1
- Finset.mul_prod_Ioo_eq_prod_Iocproof · cited by 1