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;

theorem Th14:
  the carrier of _bool SA = bool the carrier of SA
proof
  the transition-system of _bool SA = _bool the transition-system of SA by Def3
;
  hence thesis by Def1;
end;
