theorem
  a=0_goto l in rng p or a>0_goto l in rng p implies FirstNotUsed p <> a
proof
  assume a=0_goto l in rng p or a>0_goto l in rng p;
  then consider i being Instruction of SCM+FSA such that
A1: i in rng p and
A2: i = a=0_goto l or i = a>0_goto l;
  UsedIntLoc i = {a} by A2,Th16;
  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;
