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;
reserve L for finite Subset of Int-Locations;

theorem Th23:
 for n being Nat holds
  min ((RWNotIn-seq L).n) < min ((RWNotIn-seq L).(n+1))
proof let n be Nat;
  set RL = RWNotIn-seq L;
  set sn = RL.n;
  set sn1 = RL.(n+1);
  assume
A1: min ((RWNotIn-seq L).n) >= min ((RWNotIn-seq L).(n+1));
A2: sn1 = sn \ {min sn} by Def5;
  then min sn <= min sn1 by XBOOLE_1:36,XXREAL_2:60;
  then min sn = min sn1 by A1,XXREAL_0:1;
  then
A3: min sn1 in {min sn} by TARSKI:def 1;
  min sn1 in sn1 by XXREAL_2:def 7;
  hence contradiction by A2,A3,XBOOLE_0:def 5;
end;
