reserve k, m for Nat,
  x, x1, x2, x3, y, y1, y2, y3, X,Y,Z for set,
  N for with_zero set;

theorem
  for S being halting with_explicit_jumps
  IC-Ins-separated non empty
  with_non-empty_values AMI-Struct over N,
  I being Instruction of S st I is ins-loc-free holds JUMP I is empty
proof
  let S be halting with_explicit_jumps IC-Ins-separated
   non empty with_non-empty_values AMI-Struct over N,
  I be Instruction of S such that
A1: JumpPart I is empty;
A2: rng JumpPart I = {} by A1;
   JUMP I c= rng JumpPart I by Def1;
  hence thesis by A2;
end;
