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 Th10:
  for N,T holds T is InsLoc-antisymmetric
proof let N,T;
  let l1, l2 be Element of NAT;
  assume
A1: l1 <= l2, T & l2 <= l1, T;
  reconsider T as weakly_standard IC-Ins-separated non empty
  with_non-empty_values AMI-Struct over N;
  reconsider l1, l2 as Element of NAT;
  locnum(l1,T) <= locnum(l2,T) & locnum(l2,T) <= locnum(l1,T) by A1,Th9;
  hence thesis by Th7,XXREAL_0:1;
end;
