reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem Th52:
  for f,g being Function holds
  f tolerates g iff ex h being Function st f c= h & g c= h
proof
  let f,g be Function;
  thus f tolerates g implies ex h being Function st f c= h & g c= h
  proof
    assume f tolerates g;
    then reconsider h = f \/ g as Function by Th1;
    take h;
    thus thesis by XBOOLE_1:7;
  end;
  given h being Function such that
A1: f c= h & g c= h;
  f \/ g is Function by A1,GRFUNC_1:1,XBOOLE_1:8;
  hence thesis by Th51;
end;
