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
  id the carrier of OAS is dilatation
proof
  for x,y
   holds x,y '||' (id the carrier of OAS).x,(id the carrier of OAS).y
   by DIRAF:19;
  hence thesis by Th34;
end;
