Theorems · Theorem · logic and foundations

Order.enum_eq_iff

∀ {α : Type u_1} [inst : LinearOrder α] [inst_1 : WellFoundedLT α] [inst_2 : IsRegularCardinalOrder α] {s : Set α}
  {hs : IsCofinal s} {f : α → α}, Subtype.val ∘ ⇑(Order.enum s hs) = f ↔ StrictMono f ∧ Set.range f = s

A characterization of Order.enum s _: it is the unique strictly monotone function with range s.

Defined in

Mathlib.SetTheory.Cardinal.Cofinality.Enum

Cited by

1 results in Mathlib

Foundations

Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

LinearOrderWellFoundedLTIsRegularCardinalOrder