reserve x for set,
  D for non empty set,
  k, n for Element of NAT,
  z for Nat;
reserve N for with_zero set,
  S for
    IC-Ins-separated non empty with_non-empty_values AMI-Struct over N,
  i for Element of the InstructionsF of S,
  l, l1, l2, l3 for Element of NAT,
  s for State of S;
reserve ss for Element of product the_Values_of S;
reserve T for weakly_standard
 IC-Ins-separated non empty
  with_non-empty_values AMI-Struct over N;

theorem
  for l being Element of NAT, i being Element of the
  InstructionsF of STC N st InsCode i = 1 holds NIC(i, l) = {NextLoc(l,STC N)}
proof
  let l be Element of NAT, i be Element of the InstructionsF of
  STC N;
  assume
A1: InsCode i = 1;
  set M = STC N;
  consider k being Nat such that
A2: l = il.(M,k) by Th6;
  k = locnum(l,M) by A2,Def5;
  then NextLoc(l,STC N) = k+1 by Th17;
  hence thesis by A1,A2,Lm3,Th17;
end;
