
theorem Th34:
  for S being non empty reflexive RelStr
  for D being non empty directed Subset of S
  for i,j being Element of Net-Str D
  holds i <= j iff (Net-Str D).i <= (Net-Str D).j
proof
  let S be non empty reflexive RelStr;
  let D be non empty directed Subset of S;
A1: dom id D = D;
  rng id D = D;
  then reconsider g = id D as Function of D, the carrier of S
  by A1,FUNCT_2:def 1,RELSET_1:4;
  (id the carrier of S)|D = id D by FUNCT_3:1;
  then Net-Str D = Net-Str (D, g) by WAYBEL17:9;
  hence thesis by WAYBEL11:def 10;
end;
