Theorems · Theorem · logic and foundations

Order.isNormal_enum_iff_isClub

∀ {α : Type v} [inst : LinearOrder α] [inst_1 : WellFoundedLT α] [inst_2 : IsRegularCardinalOrder α] {s : Set α}
  {hs : IsCofinal s}, Order.IsNormal (Subtype.val ∘ ⇑(Order.enum s hs)) ↔ IsClub s

Club sets in regular cardinals correspond one to one with normal functions.

Defined in

Mathlib.SetTheory.Cardinal.Cofinality.Club

Cited by

1 results in Mathlib

Foundations

Depth 89 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLTIsRegularCardinalOrder