reserve x for set,
  m,n for Nat,
  a,b,c for Int_position,
  i for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l1 for Nat,
  I,J for Program of SCMPDS,
  N for with_non-empty_elements set;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem
 for s being 0-started State of SCMPDS
 for I being parahalting halt-free Program of SCMPDS,J being
  parahalting shiftable Program of SCMPDS holds IExec(I ';' J,P,s).a
   = IExec(J,P,Initialize IExec(I,P,s)).a
proof
  let s be 0-started State of SCMPDS;
  let I be parahalting halt-free Program of SCMPDS,J be parahalting
  shiftable Program of SCMPDS;
A1: not a in
 dom Start-At(IC IExec(J,P,Initialize IExec(I,P,s)) + card I,SCMPDS)
by SCMPDS_4:18;
  IExec(I ';' J,P,s) = IncIC(IExec(J,P,Initialize IExec(I,P,s)),card I)
   by Th22;
  hence thesis by A1,FUNCT_4:11;
end;
