reserve J,J1,K for Element of Segm 13,
  b,b1,b2,c,c1,c2 for Element of SCM+FSA-Data-Loc,
  f,f1,f2 for Element of SCM+FSA-Data*-Loc;
reserve k for Nat,
  J,K,L for Element of Segm 13,
  O,P,R for Element of Segm 9;
reserve da for Int-Location,
  fa for FinSeq-Location,
  x,y for set;

theorem Th4:
  for fl being FinSeq-Location ex i being Nat st fl =
  fsloc i
proof
  let fl be FinSeq-Location;
A1: fl in SCM+FSA-Data*-Loc by Def3;
  then consider k being Nat such that
A2: fl = k or fl = -k by INT_1:def 1;
  k <> 0 by A1,A2,XBOOLE_0:def 5;
  then consider i being Nat such that
A3: k = i+1 by NAT_1:6;
  reconsider i as Nat;
  take i;
  thus thesis by A1,A2,A3,XBOOLE_0:def 5;
end;
