reserve x, y, X for set;
reserve E for non empty set;
reserve e for Element of E;
reserve u, u1, v, v1, v2, w, w9, w1, w2 for Element of E^omega;
reserve F for Subset of E^omega;
reserve i, k, l for Nat;
reserve TS for non empty transition-system over F;
reserve S, T for Subset of TS;
reserve SA for non empty semiautomaton over F;
reserve A for non empty automaton over F;
reserve p, q for Element of A;

theorem Th16:
  the carrier of _bool A = bool the carrier of A
proof
  the semiautomaton of _bool A = _bool the semiautomaton of A by Def6;
  hence thesis by Th14;
end;
