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
  for f,g being PartFunc of X,Y st TotFuncs f meets TotFuncs g holds f
  tolerates g
proof
  let f,g be PartFunc of X,Y;
  set h = the Element of TotFuncs f /\ TotFuncs g;
  assume
A1: TotFuncs f /\ TotFuncs g <> {};
  then
A2: h in TotFuncs f by XBOOLE_0:def 4;
A3: h in TotFuncs g by A1,XBOOLE_0:def 4;
  reconsider h as PartFunc of X,Y by A2,Th69;
A4: g tolerates h by A3,Th71;
  f tolerates h by A2,Th71;
  hence thesis by A2,A4,Th67,Th70;
end;
