Theorems · Theorem · order theory
Finset.Ioc_subset_Ioc
∀ {α : Type u_2} {a₁ a₂ b₁ b₂ : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α],
a₂ ≤ a₁ → b₁ ≤ b₂ → Finset.Ioc a₁ b₁ ⊆ Finset.Ioc a₂ b₂- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 59 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.Iocstatement · cited by 301
- Finset.coe_Iocproof · cited by 55
- Set.Ioc_subset_Iocproof · cited by 10
Cited by3
Results whose statement or proof uses this declaration.
- Finset.Ioc_subset_Ioc_rightproof · cited by 3
- Finset.Ioc_subset_Ioc_leftproof · cited by 2
- Chebyshev.psi_monoproof · cited by 0