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;
reserve A,B for set;
reserve x,y,i,j,k for object;
reserve x for set;
reserve x for object;

theorem
  for f,g,h being Function st f tolerates g & g tolerates h & h
  tolerates f holds f+*g tolerates h
proof
  let f,g,h be Function such that
A1: f tolerates g and
A2: g tolerates h and
A3: h tolerates f;
  let x be object;
  assume
A4: x in (dom (f+*g)) /\ dom h;
  then x in dom (f+*g) by XBOOLE_0:def 4;
  then
A5: x in dom f or x in dom g by Th12;
  x in dom h by A4,XBOOLE_0:def 4;
  then
  x in (dom h) /\ dom f & (f+*g).x = f.x or x in (dom g) /\ dom h & (f+*g)
  .x = g.x by A1,A5,Th13,Th15,XBOOLE_0:def 4;
  hence thesis by A2,A3;
end;
