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 Th14:
  for s being 0-started State of SCMPDS
  for I being parahalting halt-free Program of SCMPDS st I c= P
   holds IC Comput(P,s,LifeSpan(P +* stop I,s)) =  card I
proof
  let s be 0-started State of SCMPDS;
  let I be parahalting halt-free Program of SCMPDS;
  set PP = P +* stop I, m=LifeSpan(PP,s);
A1: stop I c= PP by FUNCT_4:25;
A2: stop I +* PP = PP & PP +* stop I = PP by A1,FUNCT_4:97;
  assume I c= P;
  hence IC Comput(P,s,m) = IC Comput(PP,s,m) by Th13
    .= card I by Th11,A2,FUNCT_4:25;
end;
