Theorems · Theorem · order theory
Finset.uIcc_subset_uIcc
∀ {α : Type u_2} [inst : Lattice α] [inst_1 : LocallyFiniteOrder α] {a₁ a₂ b₁ b₂ : α},
a₁ ∈ Finset.uIcc a₂ b₂ → b₁ ∈ Finset.uIcc a₂ b₂ → Finset.uIcc a₁ b₁ ⊆ Finset.uIcc a₂ b₂- Defined in
- Mathlib.Order.Interval.Finset.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- LatticeLocallyFiniteOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Finsetstatement · cited by 13,712
- Latticestatement and proof · cited by 916
- LocallyFiniteOrderstatement and proof · cited by 658
- sup_leproof · cited by 159
- le_infproof · cited by 107
- Finset.uIccstatement and proof · cited by 84
- Finset.Icc_subset_Iccproof · cited by 6
- Finset.mem_uIccproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- Finset.uIcc_subset_uIcc_iff_memproof · cited by 0
- Finset.uIcc_subset_uIcc_leftproof · cited by 0
- Finset.uIcc_subset_uIcc_rightproof · cited by 0