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 (Y = {} implies X = {}) & f tolerates
  g holds TotFuncs f meets TotFuncs g
proof
  let f,g be PartFunc of X,Y;
  assume ( Y = {} implies X = {})& f tolerates g;
  then consider h being PartFunc of X,Y such that
A1: h is total & f tolerates h & g tolerates h by Th68;
  h in TotFuncs f & h in TotFuncs g by A1,Def5;
  hence TotFuncs f /\ TotFuncs g <> {} by XBOOLE_0:def 4;
end;
