reserve m,n for Nat,
  a for Int_position,
  i,j for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1 for Integer,
  loc for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2 for Instruction-Sequence of SCMPDS;

theorem
  for s being 0-started State of SCMPDS, i being No-StopCode parahalting
Instruction of SCMPDS,J being parahalting shiftable Program of SCMPDS, a being
  Int_position
     holds IExec(i ';' J,P,s).a = IExec(J,P,Initialize Exec(i,s)).a
proof
  let s be 0-started State of SCMPDS,
      i be No-StopCode parahalting Instruction of SCMPDS,
  J be parahalting shiftable Program of SCMPDS, a be Int_position;
  thus IExec(i ';' J,P,s).a = IExec(Load i ';' J,P,s).a
    .= IExec(J,P,Initialize IExec(Load i,P,s)).a by SCMPDS_5:35
    .= IExec(J,P,Initialize Exec(i,s)).a by SCMPDS_5:40;
end;
