Theorems · Theorem · order theory
Set.uIcc_subset_uIcc_iff_le
∀ {α : Type u_1} [inst : LinearOrder α] {a₁ a₂ b₁ b₂ : α},
Set.uIcc a₁ b₁ ⊆ Set.uIcc a₂ b₂ ↔ min a₂ b₂ ≤ min a₁ b₁ ∧ max a₁ b₁ ≤ max a₂ b₂- Cited by
- 3 results in Mathlib
- Foundations
- Depth 17 from the axioms · uses propext
- Assumes
- LinearOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- LinearOrderstatement and proof · cited by 8,572
- Set.uIccstatement · cited by 393
- Set.uIcc_subset_uIcc_iff_le'proof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- Set.abs_sub_le_of_uIcc_subset_uIccproof · cited by 3
- Function.Periodic.intervalIntegrableproof · cited by 2
- Set.uIoc_subset_uIoc_of_uIcc_subset_uIccproof · cited by 1