reserve G for non empty DTConstrStr,
  s for Symbol of G,
  n,m for String of G;
reserve n1,n2,n3 for String of G;

theorem
  for G being non empty GrammarStr, n being String of G holds n in Lang(
  G) iff rng n c= Terminals(G) & n is_derivable_from <*the InitialSym of G*>
proof
  let G be non empty GrammarStr, n be String of G;
  now
    assume n in Lang G;
    then ex a being Element of (the carrier of G)* st n = a & rng a c=
    Terminals(G) & a is_derivable_from <*the InitialSym of G*>;
    hence rng n c= Terminals(G) & n is_derivable_from <*the InitialSym of G*>;
  end;
  hence thesis;
end;
