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

theorem Th2:
  for S being standard IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N, I being Instruction of S
  st for f being Element of NAT holds NIC(I,f)={f+1}
  holds JUMP I is empty
proof
  let S be standard IC-Ins-separated
  non empty with_non-empty_values AMI-Struct over N, I be Instruction of S;
  assume
A1: for f being Element of NAT holds NIC(I,f)={f+1};
  set p=1, q=2;
  reconsider p,q as Element of NAT;
  set X = the set of all  NIC(I,f) where f is Nat;
  assume not thesis;
  then consider x being object such that
A2: x in meet X;
A3: NIC(I,p) = {p+1} by A1;
A4: NIC(I,q) = {q+1} by A1;
A5: {succ p} in X by A3;
A6: {succ q} in X by A4;
A7: x in {succ p} by A2,A5,SETFAM_1:def 1;
A8: x in {succ q} by A2,A6,SETFAM_1:def 1;
    x = succ p by A7,TARSKI:def 1;
  hence contradiction by A8,TARSKI:def 1;
end;
