Theorems · Theorem · order theory
Set.Ioo_subset_Ioo_right
∀ {α : Type u_1} [inst : Preorder α] {a₁ a₂ b : α}, a₂ ≤ a₁ → Set.Ioo b a₂ ⊆ Set.Ioo b a₁- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 8 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_rflproof · cited by 1,558
- Set.Ioostatement · cited by 1,214
- Set.Ioo_subset_Iooproof · cited by 19
Cited by2
Results whose statement or proof uses this declaration.
- Ioo_mem_nhdsLT_of_memproof · cited by 4
- Real.lt_tanproof · cited by 2