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;
