theorem Th54:
  a in K & b in K & a<>b & K is being_line implies K =Line(a,b)
proof
  assume that
A1: a in K & b in K & a<>b and
A2: K is being_line;
  reconsider a9=a,b9=b as Element of the AffinStruct of POS;
  reconsider K9=K as Subset of the AffinStruct of POS;
  K9 is being_line by A2,Th43;
  then K9 = Line(a9,b9) by A1,AFF_1:57;
  hence thesis by Th41;
end;
