Theorems · Theorem · order theory
Set.Icc_subset_Icc_iff
∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b₁ b₂ : α}, a₁ ≤ b₁ → (Set.Icc a₁ b₁ ⊆ Set.Icc a₂ b₂ ↔ a₂ ≤ a₁ ∧ b₁ ≤ b₂)- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Preorderstatement and proof · cited by 7,952
- LE.le.transproof · cited by 3,151
- Set.Iccstatement and proof · cited by 1,702
- le_rflproof · cited by 1,558
Cited by5
Results whose statement or proof uses this declaration.
- sum_mul_eq_sub_sub_integral_mulproof · cited by 4
- BoxIntegral.Box.le_TFAEproof · cited by 2
- Set.uIcc_subset_uIcc_iff_le'proof · cited by 1
- ciSup_mem_iInter_Icc_of_antitone_Iccproof · cited by 1
- Finset.Icc_subset_Icc_iffproof · cited by 1