theorem
  for f being Permutation of the carrier of OAS st f is
  positive_dilatation holds f" is positive_dilatation
proof
  let f be Permutation of the carrier of OAS;
  assume f is positive_dilatation;
  then
A1: f is_DIL_of OAS;
  OAS is CongrSpace by Th26;
  then f" is_DIL_of OAS by A1,Th24;
  hence thesis;
end;
