reserve A for non empty set,
  a,b,x,y,z,t for Element of A,
  f,g,h for Permutation of A;
reserve R for Relation of [:A,A:];
reserve AS for non empty AffinStruct;
reserve a,b,x,y for Element of AS;
reserve CS for CongrSpace;
reserve OAS for OAffinSpace;
reserve a,b,c,d,p,q,r,x,y,z,t,u for Element of OAS;
reserve f,g for Permutation of the carrier of OAS;

theorem
  f is negative_dilatation implies f" is negative_dilatation
proof
  assume
A1: f is negative_dilatation;
  let x,y;
  set x9=f".x, y9=f".y;
  f.x9=x & f.y9=y by Th2;
  then y9,x9 // x,y by A1;
  hence thesis by DIRAF:2;
end;
