Theorems · Theorem · order theory
Finset.coe_Ioo
∀ {α : Type u_1} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α] (a b : α), ↑(Finset.Ioo a b) = Set.Ioo a b- Defined in
- Mathlib.Order.Interval.Finset.Defs
- Cited by
- 48 results in Mathlib
- Foundations
- Depth 56 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 · cited by 8,199
- Preorderstatement and proof · cited by 7,952
- Set.extproof · cited by 2,266
- Set.Ioostatement · cited by 1,214
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Ioostatement · cited by 185
- Finset.mem_Iooproof · cited by 13
Cited by48
Results whose statement or proof uses this declaration.
- Fin.map_castLEEmb_Iooproof · cited by 2
- Finset.Ioo_insert_leftproof · cited by 2
- Finset.Ioo_insert_rightproof · cited by 2
- Finset.Ioo_subset_Ico_selfproof · cited by 2
- Finset.Ioo_subset_Iooproof · cited by 2
- Fin.map_castAddEmb_Ioiproof · cited by 1
- Finset.map_add_left_Iooproof · cited by 1
- Finset.Ioc_pred_right_eq_Iooproof · cited by 1
- Finset.Ioc_sdiff_Ioo_selfproof · cited by 1
- Finset.map_add_right_Iooproof · cited by 1
- Fin.finsetImage_addNat_Iooproof · cited by 1
- Fin.map_finCongr_Iooproof · cited by 1