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 holds dom s = {IC SCMPDS} \/ SCM-Data-Loc
 proof
  let s be State of SCMPDS;
   dom s = the carrier of SCMPDS by PARTFUN1:def 2;
   hence thesis by SCMPDS_2:84,STRUCT_0:4;
 end;
