theorem Satz4p18:
  a <> b & Collinear a,b,c & a,c equiv a,c9 & b,c equiv b,c9 implies c = c9
  proof
    assume a <> b & Collinear a,b,c & a,c equiv a,c9 & b,c equiv b,c9;
    then c,c equiv c,c9 by Satz4p17;
    hence thesis by Satz2p2,GTARSKI1:def 7;
  end;
