Theorems · Theorem · order theory
Finset.Ico_filter_lt_of_le_left
∀ {α : Type u_2} {a b c : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α]
[inst_2 : DecidablePred fun x => x < c], c ≤ a → {x ∈ Finset.Ico a b | x < c} = ∅- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 1 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 · cited by 13,712
- Preorderstatement and proof · cited by 7,952
- LE.le.transproof · cited by 3,151
- Finset.filterstatement · cited by 949
- LocallyFiniteOrderstatement and proof · cited by 658
- Finset.Icostatement and proof · cited by 450
- LE.le.not_gtproof · cited by 189
- Finset.mem_Icoproof · cited by 50
- Finset.filter_false_of_memproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Multiset.Ico_filter_lt_of_le_leftproof · cited by 0