Theorems · Theorem · order theory
IsMax.Ici_eq
∀ {α : Type u_1} [inst : PartialOrder α] {a : α}, IsMax a → Set.Ici a = {a}- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
- Assumes
- PartialOrder
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- PartialOrderstatement and proof · cited by 6,410
- Set.Icistatement · cited by 1,070
- IsMaxstatement and proof · cited by 372
- Set.self_mem_Iicproof · cited by 26
- Set.eq_singleton_iff_unique_memproof · cited by 20
- IsMax.eq_of_geproof · cited by 7
Cited by3
Results whose statement or proof uses this declaration.
- Set.Ici_topproof · cited by 4
- exists_Icc_mem_subset_of_mem_nhdsGEproof · cited by 2
- PredOrder.isOpen_singleton_iffproof · cited by 2