reserve R for Ring,
  r for Element of R,
  a, b, d1, d2 for Data-Location of R,
  il, i1, i2 for Nat,
  I for Instruction of SCM R,
  s,s1, s2 for State of SCM R,
  T for InsType of the InstructionsF of SCM R,
  k for Nat;

theorem
  for o being Object of SCM R
   holds o = IC SCM R or o is Data-Location of R
proof
  let o be Object of SCM R;
  assume o <> IC SCM R;
  then not o in {IC SCM R} by TARSKI:def 1;
  then
A1: not o in {NAT} by SCMRING2:8;
  not o in {NAT} by A1;
  then o in (the carrier of SCM R) \ ({NAT}) by XBOOLE_0:def 5;
  then o in SCM-Data-Loc by SCMRING2:25;
 hence thesis by AMI_2:def 16;
