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 Th26:
  for F being lower non empty
   NAT-defined (the InstructionsF of T)-valued finite Function
   holds il.(T,0) in dom F
proof
  let F be lower non empty
   NAT-defined (the InstructionsF of T)-valued finite Function;
  consider l being object such that
A1: l in dom F by XBOOLE_0:def 1;
  reconsider l as Element of NAT by A1;
  consider f being sequence of NAT such that
A2: f is bijective and
A3: for m, n being Element of NAT holds m <= n iff f.m <= f.n, T and
A4: il.(T,0) = f.0 by Def4;
  rng f = NAT by A2,FUNCT_2:def 3;
  then consider x being object such that
A5: x in dom f and
A6: l = f.x by FUNCT_1:def 3;
  reconsider x as Element of NAT by A5;
  f.0 <= f.x, T by A3;
  hence thesis by A1,A4,A6,Def10;
end;
