
theorem Th4:
  for s being State of SCM, t being Terminal of SCM-AE holds
  (root-tree t)@s = s.t
proof
  let s be State of SCM, t be Terminal of SCM-AE;
  ex f being Function of TS SCM-AE, INT st (root-tree t)@s = f.(root-tree
  t) & (for t being Terminal of SCM-AE holds f.(root-tree t) = s.t) & for nt
  being NonTerminal of SCM-AE, tl, tr being bin-term, rtl, rtr being Symbol of
SCM-AE st rtl = root-label tl & rtr = root-label tr & nt ==> <* rtl, rtr *> for
xl, xr being Element of INT st xl = f.tl & xr = f.tr holds f.(nt-tree (tl, tr))
  = nt-Meaning_on (xl, xr) by Def9;
  hence thesis;
end;
