reserve V, C for set;

theorem Th1:
  {} in SubstitutionSet (V, C)
proof
  {} c= PFuncs (V,C);
  then
A1: {} in Fin PFuncs (V,C) by FINSUB_1:def 5;
  ( for u being set st u in {} holds u is finite)& for s, t being Element
  of PFuncs (V, C) holds ( s in {} & t in {} & s c= t implies s = t );
  hence thesis by A1;
end;
