theorem :: AMISTD_1:21

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