reserve x for set,
  m,n for Nat,
  a,b for Int_position,
  i,j,k for Instruction of SCMPDS,
  s,s1,s2 for State of SCMPDS,
  k1,k2 for Integer,
  loc,l for Nat,
  I,J,K for Program of SCMPDS;
reserve P,P1,P2,Q for Instruction-Sequence of SCMPDS;

theorem Th25: ::SCMPDS_6:42
  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 ';' J),Comput(P+*stop(I ';' J),s,k))
   <> halt SCMPDS
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),
  m= LifeSpan(P1,s), s3=Comput(P2,s,k), P3 = P2;
  assume that
A1: I is_closed_on s,P and
A2: I is_halting_on s,P and
A3: k < m;
  assume CurInstr(P3,s3) = halt SCMPDS;
  then
A4: CurInstr(P1,Comput(P1,s,k)) = halt SCMPDS by A1,A2,A3,SCMPDS_6:27;
  Initialize s = s by MEMSTR_0:44;
  then P1 halts_on s by A2,SCMPDS_6:def 3;
  hence thesis by A3,A4,EXTPRO_1:def 15;
end;
