Theorems · Theorem · order theory
Set.Iic_disjoint_Ioi
∀ {α : Type v} [inst : Preorder α] {a b : α}, a ≤ b → Disjoint (Set.Iic a) (Set.Ioi b)- Defined in
- Mathlib.Order.Interval.Set.Disjoint
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 60 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Preorder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Disjointstatement · cited by 2,201
- Set.Ioistatement and proof · cited by 1,463
- Set.Iicstatement and proof · cited by 1,111
- LE.le.trans_ltproof · cited by 795
- LT.lt.not_geproof · cited by 305
- Set.disjoint_leftproof · cited by 121
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.integral_of_hasDerivAt_of_tendstoproof · cited by 4
- integral_comp_absproof · cited by 2
- Set.Iic_disjoint_Iocproof · cited by 2
- Filter.disjoint_atTop_principal_Iicproof · cited by 1
- intervalIntegral.integral_Iic_add_Ioiproof · cited by 0
- Filter.disjoint_atBot_principal_Ioiproof · cited by 0