reserve N for with_zero set;

theorem
  for A being standard IC-Ins-separated non empty
  with_non-empty_values AMI-Struct over N, I being Instruction of A st I is
  sequential holds IC A in Output I
proof
  let A be standard 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).IC A = IC s + 1;
  set s = the State of A;
  Exec(I,s).IC A = IC s + 1 by A1;
  then Exec(I,s).IC A <> IC s by NAT_1:16;
  hence thesis by Def3;
end;
