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 Th8:
 for s being 0-started State of SCMPDS
 for I being parahalting Program of SCMPDS, J being Program of SCMPDS
   st stop I c= P
 for m st m <= LifeSpan(P,s)
 holds  Comput(P,s,m) =  Comput(P+*stop(I ';' J), s,m)
proof
  let s be 0-started State of SCMPDS;
  let I be parahalting Program of SCMPDS, J be Program of SCMPDS;
  assume
A1: stop I c= P;
  set sIJ=stop (I ';' J), SS=Stop SCMPDS;
  let m;
  assume
A2: m <= LifeSpan(P,s);
  P +* sIJ = P +* (I ';' (J ';' SS)) by AFINSQ_1:27;
  hence thesis by A1,A2,Th7;
end;
