Theorems · Theorem · order theory
IsMin.Iio_eq
∀ {α : Type u_1} [inst : Preorder α] {a : α}, IsMin a → Set.Iio a = ∅Alias of the reverse direction of Set.Iio_eq_empty_iff.
- Defined in
- Mathlib.Order.Interval.Set.Basic
- Cited by
- 11 results in Mathlib
- Foundations
- Depth 26 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.
Cites5
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
- Set.Iiostatement · cited by 1,166
- IsMinstatement · cited by 277
- Set.Iio_eq_empty_iffproof · cited by 5
Cited by11
Results whose statement or proof uses this declaration.
- Order.IsSuccPrelimit.sSup_Iioproof · cited by 4
- nhds_bot_orderproof · cited by 4
- PredOrder.nhdsLTproof · cited by 3
- Fin.isAddFreimanIso_Iioproof · cited by 3
- coeff_minpolyDiv_sub_pow_mem_spanproof · cited by 1
- BoundedVariationOn.eVariationOn_Iic_eq_Iio_add_edistproof · cited by 1
- Set.Iio_botproof · cited by 1
- Module.exists_isPrincipal_quotient_of_finiteproof · cited by 1
- Set.Iio_Falseproof · cited by 0
- ProbabilityTheory.map_cast_binomial_zeroproof · cited by 0
- ProbabilityTheory.binomial_zeroproof · cited by 0