reserve A,B,a,b,c,d,e,f,g,h for set;

theorem Th23:
  for G being non empty RelStr, H being non empty full SubRelStr
  of G st G is N-free holds H is N-free
proof
  let G be non empty RelStr, H be non empty full SubRelStr of G;
  assume
A1: G is N-free;
A2: G embeds H by Th22;
  assume not thesis;
  then H embeds Necklace 4 by NECKLA_2:def 1;
  then G embeds Necklace 4 by A2,NECKLACE:12;
  hence contradiction by A1,NECKLA_2:def 1;
end;
