Theorems · Theorem · order theory
Finset.coe_Ioc
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] (b a : α), ↑(Finset.Ioc b a) = Set.Ioc b a- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 55 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- PreorderLocallyFiniteOrder
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.
- Setstatement · cited by 53,352
- Finsetstatement · cited by 13,712
- SetLike.coestatement and proof · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Set.extproof · cited by 2,266
- Set.Iocstatement · cited by 971
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Iocstatement and proof · cited by 301
- Finset.mem_Ioc'proof · cited by 3
Cited by55
Results whose statement or proof uses this declaration.
- Finset.Ioc_subset_Iic_selfproof · cited by 12
- Finset.Ioc_subset_Iocproof · cited by 3
- Finset.Ioc_union_Ioc_eq_Iocproof · cited by 3
- Fin.map_castLEEmb_Iocproof · cited by 2
- Finset.insert_Ioc_right_eq_Ioc_succ_of_not_isMaxproof · cited by 2
- Finset.Ioo_insert_rightproof · cited by 2
- Finset.Icc_succ_left_eq_Iocproof · cited by 2
- Finset.Ioc_eq_empty_iffproof · cited by 2
- Finset.insert_Ioc_left_eq_Ioc_predproof · cited by 1
- Finset.insert_Ioc_left_eq_Ioc_pred_of_not_isMinproof · cited by 1
- Finset.Ioc_pred_left_eq_Iccproof · cited by 1
- Finset.Ioc_pred_left_eq_Icc_of_not_isMinproof · cited by 1