theorem
  a,b _|_ K implies ex p st LIN a,b,p & p in K
proof
  assume a,b _|_ K;
  then consider p,q such that
  p<>q and
A1: K = Line(p,q) and
A2: a,b _|_ p,q;
  consider c such that
A3: LIN a,b,c and
A4: LIN p,q,c by A2,Th67;
  c in K by A1,A4,Def10;
  hence thesis by A3;
end;
