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 Th23: :: SCMPDS_5:30
  for I be halt-free Program of SCMPDS,J be Program of SCMPDS st
  I c= J & I is_closed_on s,P & I is_halting_on s,P
   holds IC Comput(P+*J, Initialize s,
    LifeSpan(P +* stop I,Initialize s)) =  card I
proof
  let I be halt-free Program of SCMPDS,J be Program of SCMPDS;
  set s1 = Initialize s, P1 = P +* J,
  ss = Initialize s,
  PP = P +* stop I,
  m=LifeSpan(PP,ss);
  assume that
A1: I c= J and
A2: I is_closed_on s,P and
A3: I is_halting_on s,P;
  thus IC Comput(P1, s1,m) =IC Comput(PP, ss,LifeSpan(PP,ss)) by A1,A2,A3,Th18
    .= card I by A2,A3,SCMPDS_6:29;
end;
