ARC DSL SIMULATOR

-- apply_object_to_grid: THE MUTATION WITNESS def apply_object_to_grid {H W : ℕ} (g : ARC_Grid H W) (pixels : Finset (ARC_Cell H W)) (color : ARC_Color) : ARC_Grid H W := fun p => if p ∈ pixels then color else g p -- KEY LEMMA: g' returns color at every p ∈ pixels theorem apply_object_color ... (hp : p ∈ pixels) : apply_object_to_grid g pixels color p = color := by simp [apply_object_to_grid, hp] -- ✅ NO SORRY -- RECOLOR V2 · is_monochrome: PROVEN ✅ def recolor_object_v2 ... : ARC_Object (apply_object_to_grid g obj.pixels new_color) where is_monochrome := by intro p hp exact apply_object_color g obj.pixels new_color p hp -- ✅ ONE LINE -- TRANSLATE V2 · is_monochrome: PROVEN ✅ def translate_object_v2 ... := -- ...match translate_object... is_monochrome := by intro p hp exact apply_object_color g shifted obj.color p hp -- ✅ ONE LINE -- REMAINING SORRYS IN THIS AREA: is_connected := by exact sorry -- IRF-DSL-TRANSLATE-CONN-V2: path lifting via shift_cell bijection is_maximal := by exact sorry -- IRF-DSL-RECOLOR-MAX / TRANSLATE-MAX-V2: erase precondition