Theorems · Theorem · order theory
Set.Icc_subset_Icc
∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b₁ b₂ : α}, a₂ ≤ a₁ → b₁ ≤ b₂ → Set.Icc a₁ b₁ ⊆ Set.Icc a₂ b₂- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 27 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_transproof · cited by 985
Cited by27
Results whose statement or proof uses this declaration.
- Set.Icc_subset_uIccproof · cited by 12
- Set.Icc_subset_Icc_rightproof · cited by 8
- Finset.Icc_subset_Iccproof · cited by 6
- Set.uIcc_subset_uIccproof · cited by 6
- Set.Icc_subset_Icc_leftproof · cited by 6
- Set.uIcc_subset_Iccproof · cited by 5
- integrableOn_mul_sum_Iccproof · cited by 3
- Set.Icc_subset_uIcc'proof · cited by 3
- MeasureTheory.hittingBtwn_eq_hittingBtwn_of_existsproof · cited by 3
- intervalIntegral.sub_le_integral_of_hasDeriv_right_of_leproof · cited by 2
- RightDerivMeasurableAux.le_of_mem_Aproof · cited by 2
- Real.tendsto_Icc_vitaliFamily_leftproof · cited by 2