Theorems · Theorem · order theory
Finset.Ico_eq_empty
∀ {α : Type u_2} {a b : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], ¬a < b → Finset.Ico a b = ∅Alias of the reverse direction of Finset.Ico_eq_empty_iff.
- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 60 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icostatement · cited by 450
- Finset.Ico_eq_empty_iffproof · cited by 2
Cited by5
Results whose statement or proof uses this declaration.
- Finset.Ico_eq_empty_of_leproof · cited by 22
- Finset.card_Ico_eq_card_Icc_sub_oneproof · cited by 8
- Finset.Ico_selfproof · cited by 8
- Finset.card_Ioo_eq_card_Ico_sub_oneproof · cited by 3
- geom_sum_Ico_le_of_lt_oneproof · cited by 1