Theorems · Theorem · order theory
Set.mem_Ici_of_Ioi
∀ {α : Type u_1} [inst : Preorder α] {a x : α}, x ∈ Set.Ioi a → x ∈ Set.Ici a- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 2 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.Ioistatement and proof · cited by 1,463
- Set.Icistatement · cited by 1,070
- Set.Ioi_subset_Ici_selfproof · cited by 34
Cited by2
Results whose statement or proof uses this declaration.
- intermediate_value_Ioiproof · cited by 1
- intermediate_value_Iio'proof · cited by 1