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 Th67:
  for f,g,h being PartFunc of X,Y st f tolerates h & g tolerates
  h & h is total holds f tolerates g
proof
  let f,g,h be PartFunc of X,Y such that
A1: f tolerates h and
A2: g tolerates h and
A3: dom h = X;
  let x be object;
  assume
A4: x in dom f /\ dom g;
  then x in dom f by XBOOLE_0:def 4;
  then x in dom f /\ dom h by A3,XBOOLE_0:def 4;
  then
A5: f.x = h.x by A1;
  x in dom g by A4,XBOOLE_0:def 4;
  then x in dom g /\ dom h by A3,XBOOLE_0:def 4;
  hence thesis by A2,A5;
end;
