theorem Th12:
  for X being SetWithCompoundTerm of S,V, g being Gate of X-CircuitStr
  holds g = (g.{})-tree the_arity_of g
proof
  let X be SetWithCompoundTerm of S,V;
  let g be Gate of X-CircuitStr;
   for t being Element of X holds t is finite;
  hence thesis by TREES_9:def 13;
end;
