
theorem Th106: :: MClique0
for G being with_finite_clique# SimpleGraph st clique# G = 0
for D being finite Clique of Mycielskian G holds order D <= 1
proof
  let G be with_finite_clique# SimpleGraph such that
A1: clique# G = 0;
   set uG = union G;
A2: Vertices G = {} by A1,Th54;
A3: G is void by A2,Th28;
A4: union Mycielskian G
    = union {{},{uG}} by A3,Th88
   .= {} \/ {uG} by ZFMISC_1:75
   .= {uG};
  let D be finite Clique of Mycielskian G;
    Vertices D c= {uG} by A4,ZFMISC_1:77;
  then Segm card Vertices D c= Segm card {uG} by CARD_1:11;
  then card Vertices D <= card {uG} by NAT_1:39;
  hence order D <= 1 by CARD_1:30;
end;
