theorem Th19:
  a,b '||' c,d implies c,d '||' a,b
proof
  assume
A1: a,b '||' c,d;
  a,b '||' a,b by Th18;
  then a<>b implies c,d '||' a,b by A1,Def11;
  hence thesis by Def11;
end;
