Theorems · Theorem · order theory
Finset.Ico_self
∀ {α : Type u_2} (a : α) [inst : Preorder α] [inst_1 : LocallyFiniteOrder α], Finset.Ico a a = ∅- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 61 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.
Cites6
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
- lt_irreflproof · cited by 190
- Finset.Ico_eq_emptyproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- dist_le_Ico_sum_distproof · cited by 2
- Nat.properDivisors_oneproof · cited by 2
- edist_le_Ico_sum_edistproof · cited by 2
- discrete_gronwall_prod_generalproof · cited by 1
- Nat.image_Ico_modproof · cited by 1
- eVariationOn.add_pointproof · cited by 1
- Multiset.Ico_selfproof · cited by 0
- InnerProductSpace.gramSchmidt_botproof · cited by 0