theorem
  a,b _|_ K implies b,a _|_ K
proof
  assume a,b _|_ K;
  then consider p,q such that
A1: p<>q & K = Line(p,q) and
A2: a,b _|_ p,q;
  p,q _|_ a,b by A2,Def7;
  then p,q _|_ b,a by Def7;
  then b,a _|_ p,q by Def7;
  hence thesis by A1;
end;
