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;
reserve L for finite Subset of FinSeq-Locations;

theorem
  First*NotIn L = fsloc m & not fsloc n in L implies m <= n
proof
  assume that
A1: First*NotIn L = fsloc m and
A2: not fsloc n in L;
  consider sn being non empty Subset of NAT such that
A3: First*NotIn L = fsloc min sn and
A4: sn = {k where k is Element of NAT : not fsloc k in L} by Def4;
  n in NAT by ORDINAL1:def 12;
  then n in sn by A2,A4;
  hence thesis by A1,A3,XXREAL_2:def 7;
end;
