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;

theorem
  for S being halting IC-Ins-separated
   non empty with_non-empty_values AMI-Struct over N
 for p being non halt-free
  NAT-defined (the InstructionsF of S)-valued Function
 for d being FinPartState of S holds
  p,d computes {};
