theorem
 for N being with_zero set
 for S being IC-Ins-separated non empty with_non-empty_values AMI-Struct over N
 for F being finite preProgram of S
  holds F is really-closed iff
  for s being State of S st IC s in dom F
  for P being Instruction-Sequence of S st F c= P
   for k being Nat holds IC Comput(P,s,k) in dom F by Lm6;
