reserve i,j,k,n for Nat;
reserve x,y,z for Tuple of n, BOOLEAN;

theorem
  ChangeVal_2(i,n) = 1 implies i = 1
proof
  assume
A1: ChangeVal_2(i,n) = 1;
  assume
A2: i <> 1;
  now
    per cases;
    suppose
      i = 2 to_power(n);
      hence contradiction by A1,Def8;
    end;
    suppose
      i <> 2 to_power(n);
      hence contradiction by A1,A2,Def8;
    end;
  end;
  hence thesis;
end;
