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

theorem Th25:
  for G being non empty irreflexive RelStr holds G is N-free iff
  ComplRelStr G is N-free
proof
  let G be non empty irreflexive RelStr;
  thus G is N-free implies ComplRelStr G is N-free
  proof
    assume
A1: G is N-free;
    assume not thesis;
    then ComplRelStr G embeds Necklace 4 by NECKLA_2:def 1;
    then G embeds Necklace 4 by Th24;
    hence contradiction by A1,NECKLA_2:def 1;
  end;
  assume
A2: ComplRelStr G is N-free;
  assume not thesis;
  then G embeds Necklace 4 by NECKLA_2:def 1;
  then ComplRelStr G embeds Necklace 4 by Th24;
  hence contradiction by A2,NECKLA_2:def 1;
end;
