Theorems · Theorem · order theory
Set.Ioo_subset_Ioo
∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b₁ b₂ : α}, a₂ ≤ a₁ → b₁ ≤ b₂ → Set.Ioo a₁ b₁ ⊆ Set.Ioo a₂ b₂- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 7 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
- Set.Ioostatement and proof · cited by 1,214
- LE.le.trans_ltproof · cited by 795
- LT.lt.trans_leproof · cited by 678
Cited by19
Results whose statement or proof uses this declaration.
- HasDerivAt.lhopital_zero_right_on_Iooproof · cited by 5
- intervalIntegral.integrableOn_Ioo_rpow_iffproof · cited by 3
- Finset.Ioo_subset_Iooproof · cited by 2
- Set.Ioo_subset_Ioo_rightproof · cited by 2
- Set.ordConnected_inter_Icc_of_subsetproof · cited by 1
- Topology.isEmbedding_sigmoidproof · cited by 1
- eqOn_of_isMIntegralCurveOn_Iooproof · cited by 1
- eqOn_piecewise_of_isMIntegralCurveOn_Iooproof · cited by 1
- StrictMonoOn.exists_deriv_lt_slopeproof · cited by 1
- StrictMonoOn.exists_slope_lt_derivproof · cited by 1
- Set.Ioo_subset_Ioo_leftproof · cited by 1
- Set.Ioo_subset_uIooproof · cited by 1