reserve i, j, k for Nat,
  n for Nat,
  IL for non empty set,
  N for with_non-empty_elements set;
reserve R for non trivial Ring,
  a, b for Data-Location of R,
  loc for Nat,
  I for Instruction of SCM R,
  p for FinPartState of SCM R,
  s, s1, s2 for State of SCM R,
  P,P1,P2 for Instruction-Sequence of SCM R,
  q for FinPartState of SCM;

theorem
  for dl being Data-Location of R ex i being Nat st dl = dl.(R,i)
proof
  let dl be Data-Location of R;
  dl in Data-Locations SCM by SCMRING2:1;
  then consider i being Nat such that
A1: dl = [1,i] by AMI_2:23,AMI_3:27;
  take i;
  thus thesis by A1,Th1;
end;
