theorem
  for F being Instruction-Sequence of S
  for s being State of S, k being Nat st IC
  Comput(F,s,k) <> IC Comput(F,s,k+1) & F.(IC Comput(F,s,k+1)) = halt S
   holds LifeSpan(F,s) = k+1
proof
  let F be Instruction-Sequence of S;
  let s be State of S, k be Nat;
  assume that
A1: IC Comput(F,s,k) <> IC Comput(F,s,k+1) and
A2: F.(IC Comput(F,s,k+1)) = halt S;
A3: dom F = NAT by PARTFUN1:def 2;
  now
    assume F.(IC Comput(F,s,k)) = halt S;
    then CurInstr(F,Comput(F,s,k)) = halt S by A3,PARTFUN1:def 6;
    hence contradiction by A1,Th5,NAT_1:11;
  end;
  hence thesis by A2,Th31;
end;
