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 Th18:
  for I,J being Program of SCMPDS,
      s being 0-started State of SCMPDS, k being
  Nat st I is_closed_on s,P & I is_halting_on s,P &
   k < LifeSpan(P +* stop I,s)
 holds CurInstr(P +* stop I, Comput(P +* stop I, s,k)) =
  CurInstr(P +* stop(I ';' J),Comput(P +* stop(I ';' J),s,k))
proof
  let I,J be Program of SCMPDS,
      s be 0-started State of SCMPDS,k be Nat;
  set P1 = P +* stop I, P2 = P +* stop(I ';' J);
  set s3= Comput(P1, s,k), s4= Comput(P2, s,k),
      P3 = P1, P4 = P2,
SS=Stop SCMPDS;
  assume that
A1: I is_closed_on s,P and
A2: I is_halting_on s,P & k < LifeSpan(P1,s);
A3: Initialize s = s by MEMSTR_0:44;
    then
A4: IC s3 in dom I by A1,A2,Th17;
A5: IC s3= IC s4 by A1,A2,Th16;
A6: IC s3 in dom stop(I) by A1,A3;
A7: dom stop I c= dom stop (I ';' J) & stop (I ';' J) c= P2 by FUNCT_4:25
,SCMPDS_5:13;
A8: stop I c= P1 by FUNCT_4:25;
A9: stop (I ';' J) = I ';' J ';' SS
    .=I ';' (J ';' SS) by AFINSQ_1:27;
A10: P3/.IC s3 = P3.IC s3 by PBOOLE:143;
A11:  P4/.IC s4 = P4.IC s4 by PBOOLE:143;
  thus CurInstr(P1,s3) =P1.IC s3 by A10
    .=(stop I).IC s3 by A6,A8,GRFUNC_1:2
    .=I.IC s3 by A4,AFINSQ_1:def 3
    .=(stop (I ';' J)).IC s3 by A4,A9,AFINSQ_1:def 3
    .=P2.IC s4 by A5,A6,A7,GRFUNC_1:2
    .=CurInstr(P2,s4) by A11;
end;
