
theorem
  for V being set, C being finite set, A, B being Element of Fin PFuncs
  (V, C) st A = {} & B <> {} holds B =>> A = {}
proof
  let V be set, C be finite set, A, B be Element of Fin PFuncs (V, C);
  assume
A1: A = {} & B <> {};
  assume B =>> A <> {};
  then consider k being object such that
A2: k in B =>> A by XBOOLE_0:def 1;
  ex f being PartFunc of B, A st k = union {f.i \ i where i is Element of
  PFuncs (V, C) : i in B} & dom f = B by A2,HEYTING2:15;
  hence thesis by A1;
end;
