Theorems · Theorem · order theory
Finset.Ioo_subset_Ioo
∀ {α : Type u_2} {a₁ a₂ b₁ b₂ : α} [inst : Preorder α] [inst_1 : LocallyFiniteOrder α],
a₂ ≤ a₁ → b₁ ≤ b₂ → Finset.Ioo a₁ b₁ ⊆ Finset.Ioo a₂ b₂- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 2 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.Ioostatement · cited by 185
- Finset.coe_Iooproof · cited by 48
- Set.Ioo_subset_Iooproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Finset.Ioo_subset_Ioo_leftproof · cited by 0
- Finset.Ioo_subset_Ioo_rightproof · cited by 0