Theorems · Theorem · order theory
Set.Ico_subset_Ico
∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b₁ b₂ : α}, a₂ ≤ a₁ → b₁ ≤ b₂ → Set.Ico a₁ b₁ ⊆ Set.Ico a₂ b₂- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 5 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
- LE.le.transproof · cited by 3,151
- Set.Icostatement and proof · cited by 799
- LT.lt.trans_leproof · cited by 678
Cited by5
Results whose statement or proof uses this declaration.
- Finset.Ico_subset_Icoproof · cited by 8
- Set.Ico_subset_Ico_rightproof · cited by 6
- intervalIntegral.sum_integral_adjacent_intervals_Icoproof · cited by 4
- Set.Ico_subset_Ico_iffproof · cited by 3
- Set.Ico_subset_Ico_leftproof · cited by 2