reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;

theorem
  for f,g being PartFunc of X,Y st g c= f holds TotFuncs f c= TotFuncs g
proof
  let f,g be PartFunc of X,Y such that
A1: g c= f;
  let h be object;
  assume
A2: h in TotFuncs f;
  then reconsider h9=h as PartFunc of X,Y by PARTFUN1:69;
A3: h9 is total by A2,PARTFUN1:70;
  g tolerates h9 by A1,A2,PARTFUN1:58,71;
  hence thesis by A3,PARTFUN1:def 5;
end;
