reserve x for set,
  D for non empty set,
  k, n for 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 Nat,
  s for State of S;
reserve ss for Element of product the_Values_of S;

theorem
  for i being Instruction of STC N st InsCode i = 1 holds i is non halting
proof
  let i be Instruction of STC N;
  set M = STC N;
  set s =the  State of M;
  assume InsCode i = 1;
  then
A1: Exec(i,s).IC M = IC s + 1 by Lm3;
  assume for s being State of M holds Exec(i,s) = s;
  then Exec(i,s).IC M = IC s;
  hence thesis by A1;
end;
