reserve k for Nat,
  da,db for Int-Location,
  fa for FinSeq-Location;

theorem
  for s being State of SCM+FSA, iloc being Nat
  , a being FinSeq-Location holds s.a = (s +* Start-At(iloc,SCM+FSA)).a
proof
  let s be State of SCM+FSA, iloc be Nat, a be
  FinSeq-Location;
  a in the carrier of SCM+FSA;
  then a in dom s by PARTFUN1:def 2;
  then
A1: dom (Start-At(iloc,SCM+FSA)) = {IC SCM+FSA} &
 a in dom s \/ dom (Start-At(iloc,SCM+FSA))
  by XBOOLE_0:def 3;
  a <> IC SCM+FSA by SCMFSA_2:57;
  then not a in {IC SCM+FSA} by TARSKI:def 1;
  hence thesis by A1,FUNCT_4:def 1;
end;
