reserve N for with_zero set;

theorem Th12:
  for A being IC-Ins-separated non empty
with_non-empty_values AMI-Struct over N, I being Instruction of A
 st I is halting holds Out_U_Inp
  I is empty
proof
  let A be IC-Ins-separated non empty with_non-empty_values AMI-Struct over
  N, I be Instruction of A such that
A1: for s being State of A holds Exec(I,s) = s;
  assume not thesis;
  then consider o being Object of A such that
A2: o in Out_U_Inp I;
  consider s being State of A, a being Element of Values o such that
A3: Exec(I,s+*(o,a)) <> Exec(I,s) +* (o,a) by A2,Def5;
  Exec(I,s+*(o,a)) = s+*(o,a) by A1
    .= Exec(I,s) +* (o,a) by A1;
  hence thesis by A3;
end;
