Theorems · Theorem · order theory
Set.Ici_inter_Iic
∀ {α : Type u_1} [inst : Preorder α] {a b : α}, Set.Ici a ∩ Set.Iic b = Set.Icc a b- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 6 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.
Cited by12
Results whose statement or proof uses this declaration.
- interior_Iccproof · cited by 37
- convex_Iccproof · cited by 29
- Set.Icc_inter_Iccproof · cited by 5
- Order.Icc_succ_left_of_not_isMaxproof · cited by 2
- Order.Ico_succ_right_of_not_isMaxproof · cited by 2
- bddBelow_bddAbove_iff_subset_Iccproof · cited by 1
- Set.image_subtype_val_Ici_Iicproof · cited by 1
- MeasureTheory.IntegrableOn.continuousOn_Ici_primitive_Ioiproof · cited by 1
- Set.Icc_add_bijproof · cited by 1
- Set.Ici_sdiff_Ioiproof · cited by 1
- Set.Ici_disjoint_Iicproof · cited by 1
- Set.Icc_inter_Icc_eq_singletonproof · cited by 0