
theorem Th10:
  for nt being NonTerminal of SCM-AE, tl, tr being bin-term holds
max_Data-Loc_in(nt-tree(tl, tr)) = max(max_Data-Loc_in tl, max_Data-Loc_in tr)
proof
  let nt be NonTerminal of SCM-AE, tl, tr be bin-term;
A1: max_Data-Loc_in tl = f.tl & max_Data-Loc_in tr = f.tr by Def14,Lm4,Lm5;
  nt ==> <*root-label tl, root-label tr*> & max_Data-Loc_in(nt-tree(tl, tr
  )) = f.(nt-tree(tl, tr)) by Def1,Def14,Lm4,Lm5,Lm6;
  hence thesis by A1,Lm5;
end;
