reserve l, m, n for Nat;
reserve a,b for Int-Location,
  f for FinSeq-Location,
  s,s1,s2 for State of SCM+FSA;
reserve L for finite Subset of Int-Locations;

theorem
  FirstNotIn L = intloc m & not intloc n in L implies m <= n
proof
  consider sn being non empty Subset of NAT such that
A1: FirstNotIn L = intloc min sn & sn = {k where k is Element of NAT :
  not intloc k in L} by Def3;
A2: n in NAT by ORDINAL1:def 12;
  assume FirstNotIn L = intloc m & not intloc n in L;
  then m = min sn & n in sn by A1,AMI_3:10,A2;
  hence thesis by XXREAL_2:def 7;
end;
