reserve a,b,p,x,x9,x1,x19,x2,y,y9,y1,y19,y2,z,z9,z1,z2 for object,
   X,X9,Y,Y9,Z,Z9 for set;
reserve A,D,D9 for non empty set;
reserve f,g,h for Function;

theorem Th30:
  f tolerates g iff f \/ g = f +* g
proof
  thus f tolerates g implies f \/ g = f +* g
  proof
    assume f tolerates g;
    then
A1: f c= f +* g by Th28;
A2: f +* g c= f \/ g by Th29;
    g c= f +* g by Th25;
    then f \/ g c= f +* g by A1,XBOOLE_1:8;
    hence thesis by A2;
  end;
  thus thesis by PARTFUN1:51;
end;
