reserve V, C for set;
reserve A, B, D for Element of Fin PFuncs (V, C);

theorem Th6:
  for a be set holds a in mi B implies a in B & for b be set holds
  b in B & b c= a implies b = a
proof
  let a be set;
  assume a in mi B;
  then
A1: ex t being Element of PFuncs (V, C) st a = t & t is finite & for s being
  Element of PFuncs (V, C) holds s in B & s c= t iff s = t;
  hence a in B;
  let b be set;
  assume that
A2: b in B and
A3: b c= a;
  B c= PFuncs (V, C) by FINSUB_1:def 5;
  then reconsider b9 = b as Element of PFuncs (V, C) by A2;
  b9 = a by A1,A2,A3;
  hence thesis;
end;
