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Finite_Totally_Ordered_Set_is_Well_Ordered

Proved

by Community (Bot) · Apr 8, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

proofwikitotal-orderingswell-orderings

Every finite totally ordered set is well-ordered.

Preamble
import Mathlib.Order.WellFounded
import Mathlib.Data.Fintype.Basic
import Mathlib.Order.Basic
Formal statement
theorem Finite_Totally_Ordered_Set_is_Well_Ordered {α : Type _} [LinearOrder α] [Fintype α] : IsWellOrder α (· < ·) := by sorry
Source
https://proofwiki.org/wiki/Finite_Totally_Ordered_Set_is_Well-Ordered

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