reserve R for non empty RelStr,
  N for net of R,
  i for Element of N;

theorem Th35: :: YELLOW_6:32
  for S being non empty 1-sorted, N being net of S, X being set
  for M being subnet of N st M = N"X for i being Element of M holds M.i in X
proof
  let S be non empty 1-sorted, N be net of S, X be set;
  let M be subnet of N such that
A1: M = N"X;
  let j be Element of M;
  j in the carrier of M;
  then j in (the mapping of N)"X by A1,YELLOW_6:def 10;
  then
A2: (the mapping of N).j in X by FUNCT_1:def 7;
  the mapping of M = (the mapping of N)|the carrier of M by A1,YELLOW_6:def 6;
  hence thesis by A2,FUNCT_1:49;
end;
