Well_Ordering_Principle
Provednamed-theoremsnatural-numbersnumber-theoryordering-on-natural-numbersproofwikiwell-ordering-principlewell-orderings
Every non-empty subset of has a smallest (or '''first''') element. This is called the '''well-ordering principle'''. The '''well-ordering principle''' also holds for .
Preamble
import Mathlib.Analysis.Complex.Basic
Formal statement
theorem Well_Ordering_Principle (S : Set ℕ) (hS : S.Nonempty) : ∃ m ∈ S, ∀ n ∈ S, m ≤ n := by sorry
Source