theorem Th28:
  parallelogram a,b,c,d implies not a,b,c are_collinear & not b,a,d
  are_collinear & not c,d,a are_collinear & not d,c,b are_collinear & not a,c,b
  are_collinear & not b,a,c are_collinear & not b,c,a are_collinear & not c,a,b
  are_collinear & not c,b,a are_collinear & not b,d,a are_collinear & not a,b,d
  are_collinear & not a,d,b are_collinear & not d,a,b are_collinear & not d,b,a
  are_collinear & not c,a,d are_collinear & not a,c,d are_collinear & not a,d,c
  are_collinear & not d,a,c are_collinear & not d,c,a are_collinear & not d,b,c
  are_collinear & not b,c,d are_collinear & not b,d,c are_collinear & not c,b,d
  are_collinear & not c,d,b are_collinear
proof
  assume
A1: parallelogram a,b,c,d;
  then
A2: ( not c,d,a are_collinear)& not d,c,b are_collinear by Th27;
  ( not a,b,c are_collinear)& not b,a,d are_collinear by A1,Th27;
  hence thesis by A2,Th10;
end;
