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;
reserve a,b,c for set,
  D for non empty set,
  d for Element of D;

theorem Th11:
  Lang EmptyGrammar a = {{}}
proof
  set E = EmptyGrammar a;
A1: Terminals E = {} by Th10;
  thus Lang E c= {{}}
  proof
    let b be object;
    assume b in Lang E;
    then ex p being String of E st b = p & rng p c= Terminals E & p
    is_derivable_from <*the InitialSym of E*>;
    then b = {} by A1;
    hence thesis by TARSKI:def 1;
  end;
  let b be object;
  assume b in {{}};
  then
A2: b = {} by TARSKI:def 1;
  the Rules of E = {[a,{}]} by Def7;
  then
A3: [a,{}] in the Rules of E by TARSKI:def 1;
  the carrier of E = {a} by Def7;
  then a = the InitialSym of E by TARSKI:def 1;
  then the InitialSym of E ==> <*> the carrier of E by A3;
  then
A4: <*> the carrier of E is_derivable_from <*the InitialSym of E*> by Th3,Th7;
  rng {} = {};
  hence thesis by A1,A2,A4;
end;
