reserve N for with_zero set;

theorem
  for A being IC-Ins-separated non empty
   with_non-empty_values AMI-Struct over N, I being Instruction of A,
   o being Object
  of A st I is jump-only holds o in Output I implies o = IC A
proof
  let A be IC-Ins-separated non empty
  with_non-empty_values AMI-Struct over N, I be Instruction of A,
  o be Object of A;
  assume
A1: for s being State of A, o being Object of A, J being Instruction of
  A st InsCode I = InsCode J & o in Data-Locations A holds Exec(J,s).o = s.o;
  assume o in Output I;
  then ex s being State of A st s.o <> Exec(I,s).o by Def3;
  then
A2:  not o in Data-Locations A by A1;
   o in the carrier of A;
   then o in {IC A} \/ Data-Locations A by STRUCT_0:4;
   then o in {IC A} by A2,XBOOLE_0:def 3;
  hence thesis by TARSKI:def 1;
end;
