theorem
  for s being State of S st P halts_on s for k being Nat
    st LifeSpan(P,s) <= k
   holds CurInstr(P, Comput(P,s,k)) = halt S
proof
  let s be State of S;
  assume
  P halts_on s;
  then
A1: CurInstr(P,Comput(P,s,LifeSpan(P,s))) = halt S by Def15;
  let k be Nat;
  assume
   LifeSpan(P,s) <= k;
  hence thesis by A1,Th5;
end;
