reserve S for non empty non void ManySortedSign,
  V for non-empty ManySortedSet of the carrier of S,
  A for non-empty MSAlgebra over S,
  X for non empty Subset of S-Terms V,
  t for Element of X;

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;
