reserve N for with_zero set;
reserve N for with_zero set;
reserve x,y,z,A,B for set,
  f,g,h for Function,
  i,j,k for Nat;
reserve S for IC-Ins-separated non empty
     with_non-empty_values AMI-Struct over N,
  s for State of S;
reserve N for non empty with_zero set,
 S for IC-Ins-separated non empty with_non-empty_values AMI-Struct over N,
  s for State of S;
reserve n for Nat;
reserve N for with_zero non empty set;

theorem
  for S being IC-Ins-separated halting non empty with_non-empty_values
     AMI-Struct over N
 for P being Instruction-Sequence of S
 for s being State of S st ex k st P halts_at IC Comput(P,s,k)
   for i holds Result(P,s) = Result(P,Comput(P,s,i))
by Th8;
