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Reduced journeys preserve the movement constraints

Proved
AngelDevil.reducedJourney_is_journey

by Yuxuan Xu · Oct 18, 2026 · Mathlib 0df444a (Lean v4.33.1)

angel-problemcombinatorics

For any nonnegative integer power and any finite journey starting at the origin with each coordinate changing by at most that power per step, the earliest-predecessor reduction is again a journey with the same movement constraint. This states the structural validity of the reduction; the separate assertion about avoiding squares eaten by the transformed Devil is not included.

Preamble
import Definitions.Def_AngelDevil_ReducedJourney
Formal statement
theorem AngelDevil.reducedJourney_is_journey (p : Nat) (h : List AngelDevil.Point) (hj : AngelDevil.Journey p h) : AngelDevil.Journey p (AngelDevil.reducedJourney p h) := by sorry
Source
Mathe, The Angel of power 2 wins (2007), https://doi.org/10.1017/S0963548306008303, author manuscript p. 3, equation (1) and the paragraph immediately following it.

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