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 Th25:
  for i being Element of the InstructionsF of T
   holds il.(T,0) .--> i is lower
proof
  let i be Element of the InstructionsF of T;
  set F = il.(T,0).--> i;
  let l be Element of NAT such that
A1: l in dom F;
  let m be Element of NAT such that
A2: m <= l, T;
  consider k being Nat such that
A3: m = il.(T,k) by Th6;
A4: l = il.(T,0) by A1,TARSKI:def 1;
  then 0 <= k & k <= 0 by A2,A3,Th8;
  hence thesis by A1,A4,A3,XXREAL_0:1;
end;
