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;
reserve TS for non empty transition-system over Lex(E) \/ {<%>E};
reserve SA for non empty semiautomaton over Lex(E) \/ {<%>E};
reserve A for non empty automaton over Lex(E) \/ {<%>E};
reserve P for Subset of A;

theorem Th35:
  the InitS of _bool A = { <%>E-succ_of (the InitS of A, A) }
proof
  the InitS of _bool A = the InitS of the semiautomaton of _bool A
    .= the InitS of _bool the semiautomaton of A by Def6
    .= { <%>E-succ_of (the InitS of the semiautomaton of A, the
  semiautomaton of A) } by Def3;
  hence thesis by REWRITE3:105;
end;
