theorem
  a :=len f in rng p or f :=<0,...,0>a in rng p implies FirstNotUsed p
  <> a
proof
  assume a :=len f in rng p or f :=<0,...,0>a in rng p;
  then consider i being Instruction of SCM+FSA such that
A1: i in rng p and
A2: i = a :=len f or i = f :=<0,...,0>a;
  UsedIntLoc i = {a} by A2,Th18;
  then
A3: {a} c= UsedILoc p by A1,Th19;
  not FirstNotUsed p in UsedILoc p by Th50;
  hence thesis by A3,ZFMISC_1:31;
end;
