Theorems · Theorem · order theory
IsMin.Iic_eq
∀ {α : Type u_1} [inst : PartialOrder α] {a : α}, IsMin a → Set.Iic 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.Iicstatement · cited by 1,111
- IsMinstatement and proof · cited by 277
- Set.self_mem_Iciproof · cited by 30
- Set.eq_singleton_iff_unique_memproof · cited by 20
- IsMin.eq_of_leproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- Set.Iic_botproof · cited by 7
- SuccOrder.isOpen_singleton_iffproof · cited by 3
- exists_Icc_mem_subset_of_mem_nhdsLEproof · cited by 1