theorem
  for f,g being Permutation of the carrier of OAS st f is
positive_dilatation & g is positive_dilatation holds f*g is positive_dilatation
proof
  let f,g be Permutation of the carrier of OAS;
  assume f is positive_dilatation & g is positive_dilatation;
  then
A1: f is_DIL_of OAS & g is_DIL_of OAS;
  OAS is CongrSpace by Th26;
  then f*g is_DIL_of OAS by A1,Th25;
  hence thesis;
end;
