
theorem Th22: :: StaComplCli:
for R being RelStr, C being StableSet of ComplRelStr R holds C is Clique of R
proof
 let R be RelStr, C be StableSet of ComplRelStr R;
A1: the carrier of R = the carrier of ComplRelStr R by NECKLACE:def 8;
   now
     let a, b be Element of R such that
   A2: a in C and
   A3: b in C and
   A4: a <> b;
    reconsider ap1 = a, bp1 = b as Element of ComplRelStr R by NECKLACE:def 8;
      not ap1 <= bp1 & not bp1 <= ap1 by A2,A3,A4,DILWORTH:def 2;
     hence a <= b or b <= a by A4,A2,A1,Th18;
   end;
 hence C is Clique of R by DILWORTH:6,NECKLACE:def 8;
end;
