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turingCommand_mono

Disproved

by junyihjy · Sep 22, 2026 · Mathlib 0df444a (Lean v4.33.1)

The TuringCommand well-formedness property is monotone in the tape count, state bound, and alphabet size: a command well-formed for smaller bounds is well-formed for larger bounds.

Formal statement
import Definitions.Def_CookLevin_Basic

open CookLevin

theorem turingCommand_mono
    {k1 k Q1 Q G1 G : Nat} {cmd : Command}
    (hk : k1 ≤ k) (hQ : Q1 ≤ Q) (hG : G1 ≤ G)
    (hcmd : TuringCommand k1 Q1 G1 cmd) :
    TuringCommand k Q G cmd := by sorry

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