reserve l, m, n for Nat,
  i,j,k for Instruction of SCMPDS,
  I,J,K for Program of SCMPDS,
  p,q,r for PartState of SCMPDS;
reserve a,b,c for Int_position,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer;

theorem
  for s being State of SCMPDS, x being set st x in dom s holds x is
  Int_position or x = IC SCMPDS
proof
  set S1={IC SCMPDS}, S2=SCM-Data-Loc, S3=NAT;
  let s be State of SCMPDS;
  let x be set;
  assume
A1: x in dom s;
  dom s = the carrier of SCMPDS by PARTFUN1:def 2;
  then x in S1 \/ S2 by A1,SCMPDS_2:84,STRUCT_0:4;
  then x in S1 or x in S2 by XBOOLE_0:def 3;
  hence thesis by AMI_2:def 16,TARSKI:def 1;
end;
