Did Lincoln help build the cabin?

Did Lincoln help build his father's Goosenest Prairie cabin, a replica of which now stands on the Lincoln Log Cabin State Historic Site? It is probable that Abraham Lincoln was in Coles County in the fall of 1840 when the cabin was probably constructed, campaigning on the Whig ticket for his third term in the Illinois General Assembly. While it is impossible to pin this down with exact accuracy, tradition has Lincoln giving a speech in Charleston on September 30th; thus, it is plausible that he assisted in erecting the cabin. If he was in Coles County in late September or early October, 1840, and if Thomas Lincoln and Johnston were erecting the new cabin at that time, it is possible that Lincoln rode the seven or eight miles out to the Goosenest Prairie to assist them. However, there is no precise historical data proving he either did or did not help build the new cabin.