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;
reserve AFS for AffinSpace;
reserve a,b,c,d,d1,d2,p,x,y,z,t for Element of AFS;
reserve f,g for Permutation of the carrier of AFS;

theorem Th70:
  f is dilatation implies f" is dilatation
proof
  assume
A1: f is dilatation;
  now
    let x,y;
    set x9=f".x;
    set y9=f".y;
    f.x9=x & f.y9=y by Th2;
    then x9,y9 // x,y by A1,Th68;
    hence x,y // f".x,f".y by AFF_1:4;
  end;
  hence thesis by Th68;
end;
