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
  f tolerates g +* h implies f|(dom f \ dom h) tolerates g
proof
  assume
A1: f tolerates g +* h;
  let x be object;
  assume
A2: x in dom(f|(dom f \ dom h)) /\ dom g;
  then
A3: x in dom(f|(dom f \ dom h)) by XBOOLE_0:def 4;
  x in dom g by A2,XBOOLE_0:def 4;
  then
A4: x in dom(g +* h) by Th12;
A5: dom(f|(dom f \ dom h)) c= dom f \ dom h by RELAT_1:58;
  then x in dom f by A3,XBOOLE_0:def 5;
  then
A6: x in dom f /\ dom(g +* h) by A4,XBOOLE_0:def 4;
  not x in dom h by A3,A5,XBOOLE_0:def 5;
  then (g +* h).x = g.x by Th11;
  then f.x = g.x by A1,A6;
  hence thesis by A3,A5,FUNCT_1:49;
end;
