reserve x,y,z,X for set,
  T for Universe;

theorem Th12:
  for S being 1-sorted, N being non empty NetStr over S, M be non
empty full SubNetStr of N, x,y being Element of N, i,j being Element of M st x
  = i & y = j & x <= y holds i <= j
proof
  let S be 1-sorted, N be non empty NetStr over S, M be non empty full
  SubNetStr of N, x,y be Element of N, i,j be Element of M such that
A1: x = i & y = j & x <= y;
  reconsider M as full non empty SubRelStr of N by Def7;
  reconsider i9 = i, j9 = j as Element of M;
  i9 <= j9 by A1,YELLOW_0:60;
  hence thesis;
end;
