theorem Th39:
  parallelogram a,b,c,d implies not a,b,x are_collinear or not c,d,
  x are_collinear
proof
  assume
A1: parallelogram a,b,c,d;
  then
A2: c <>d by Th36;
  ( not a,b,c are_collinear)& a,b // c,d by A1;
  hence thesis by A2,Th28;
end;
