Theorems · Theorem · order theory
Finset.Ico_subset_Ico
∀ {α : Type u_2} {a₁ a₂ b₁ b₂ : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α],
a₂ ≤ a₁ → b₁ ≤ b₂ → Finset.Ico a₁ b₁ ⊆ Finset.Ico a₂ b₂- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 57 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
- Finset.coe_Icoproof · cited by 66
- Set.Ico_subset_Icoproof · cited by 5
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.hahn_decompositionproof · cited by 2
- Nat.Ico_filter_coprime_leproof · cited by 1
- Asymptotics.IsLittleO.sum_rangeproof · cited by 1
- discrete_gronwallproof · cited by 1
- eVariationOn.add_pointproof · cited by 1
- Finset.Ico_subset_Ico_rightproof · cited by 1
- discrete_gronwall_Icoproof · cited by 0
- Finset.Ico_subset_Ico_leftproof · cited by 0