Theorems · Theorem · order theory
Set.Iic_disjoint_Ioc
∀ {α : Type v} [inst : Preorder α] {a b c : α}, a ≤ b → Disjoint (Set.Iic a) (Set.Ioc b c)- Defined in
- Mathlib.Order.Interval.Set.Disjoint
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 61 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.
Cites9
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
- le_rflproof · cited by 1,558
- Set.Iicstatement · cited by 1,111
- Set.Iocstatement · cited by 971
- Disjoint.monoproof · cited by 69
- Set.Ioc_subset_Ioi_selfproof · cited by 24
- Set.Iic_disjoint_Ioiproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- intervalIntegral.integral_Iic_sub_Iicproof · cited by 2
- Set.Ioc_disjoint_Ioc_of_leproof · cited by 0