theorem
  a<>d implies ex b,c st parallelogram a,b,c,d
proof
  assume a<>d;
  then consider b such that
A1: not a,d,b are_collinear by Th25;
  not b,a,d are_collinear by A1,Th22;
  then consider c such that
A2: parallelogram b,a,d,c by Th44;
  parallelogram a,b,c,d by A2,Th43;
  hence thesis;
end;
