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

theorem Th11:
  for K be Element of SubstitutionSet (V, C) holds mi K = K
proof
  let K be Element of SubstitutionSet (V, C);
  thus mi K c= K by Th8;
  now
    let a be set;
    assume
A1: a in K;
    then a is finite & for b be finite set st b in K & b c= a holds b = a by
Lm1,Th5;
    hence a in mi K by A1,Th7;
  end;
  hence thesis;
end;
