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 i being Instruction of STC N, s being State of STC N st InsCode i
  = 1 holds IC Exec(i,s) = NextLoc(IC s,STC N)
proof
  let i be Instruction of STC N, s be State of STC N;
  set M = STC N;
  set k = locnum(IC s,STC N);
  reconsider K = IC s as Element of NAT;
  assume InsCode i = 1;
  then
A1: IC Exec(i,s) = IC s + 1 by Lm2
    .= K+1;
  il.(M,k) = k & il.(M,k+1) = k+1 by Th17;
  hence thesis by A1,Def5;
end;
