theorem
  a in K & b in K & a<>b & K is being_line & (a,b _|_ c,d or c,d _|_ a,b
  ) implies c,d _|_ K
proof
  assume that
A1: a in K & b in K and
A2: a<>b and
A3: K is being_line &( a,b _|_ c,d or c,d _|_ a,b);
  c,d _|_ a,b & K = Line(a,b) by A1,A2,A3,Def7,Th54;
  hence thesis by A2;
end;
