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 Th14:
  a <> b implies Terminals IterGrammar(a,b) = {b}
proof
  set T = IterGrammar(a,b);
  assume
A1: a <> b;
A2: the carrier of T = {a,b} by Def9;
  then reconsider x = a, y = b as Symbol of T by TARSKI:def 2;
A3: the Rules of T = {[a,<*b,a*>],[a,{}]} by Def9;
  thus Terminals T c= {b}
  proof
    let c be object;
    assume c in Terminals T;
    then consider s being Symbol of T such that
A4: c = s and
A5: not ex n being FinSequence st s ==> n;
    [a,<*b,a*>] in the Rules of T by A3,TARSKI:def 2;
    then x ==> <*y,x*>;
    then s <> x by A5;
    then c = b by A2,A4,TARSKI:def 2;
    hence thesis by TARSKI:def 1;
  end;
  let c be object;
  assume c in {b};
  then
A6: b = c by TARSKI:def 1;
  assume not thesis;
  then consider n being FinSequence such that
A7: y ==> n by A6;
A8: [a,{}] <> [b,n] by A1,XTUPLE_0:1;
  [a,<*b,a*>] <> [b,n] by A1,XTUPLE_0:1;
  then not [b,n] in {[a,<*b,a*>],[a,{}]} by A8,TARSKI:def 2;
  hence thesis by A3,A7;
end;
