theorem
  for s being State of SCM, iloc being Nat, a
  being Data-Location holds s.a = (s +* Start-At(iloc,SCM)).a
proof
  let s be State of SCM, iloc be Nat, a be
  Data-Location;
  a in the carrier of SCM;
  then a in dom s by PARTFUN1:def 2;
  then
A1: dom (Start-At(iloc,SCM)) = {IC SCM} &
 a in dom s \/ dom (Start-At(iloc,SCM)) by XBOOLE_0:def 3;
  a <> IC SCM by Th2;
  then not a in {IC SCM} by TARSKI:def 1;
  hence thesis by A1,FUNCT_4:def 1;
end;
