theorem Th36:
  w-succ_of ({ <%>E-succ_of (X, A) }, _bool A) = { w-succ_of (X, A ) }
proof
  set SA = the semiautomaton of A;
  set Es = <%>E-succ_of (X, A);
  the semiautomaton of _bool A = _bool SA by Def6;
  hence w-succ_of ({ Es }, _bool A) = w-succ_of ({ Es }, _bool SA) by
REWRITE3:105
    .= w-succ_of ({ <%>E-succ_of (X, SA) }, _bool SA) by REWRITE3:105
    .= { w-succ_of (X, SA) } by Th32
    .= { w-succ_of (X, A) } by REWRITE3:105;
end;
