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 ::SCMPDS_5:37
  for s being 0-started State of SCMPDS
  for I being halt-free Program of SCMPDS,J being shiftable Program of
SCMPDS st I is_closed_on s,P & I is_halting_on s,P
 & J is_closed_on IExec(I,P,s),P & J
  is_halting_on IExec(I,P,s),P
holds LifeSpan(P+*stop(I ';' J),s) =
 LifeSpan(P +* stop I,s) +
  LifeSpan(P +* stop I +* stop J,
  Initialize Result(P +* stop I,s)) by Lm1;
