
theorem Th110: :: MClique
for G being with_finite_clique# SimpleGraph
 st 2 <= clique# G holds clique# Mycielskian G = clique# G
proof
  let G be with_finite_clique# SimpleGraph such that
A1: 2 <= clique# G and
A2: clique# Mycielskian G <> clique# G;
   set MG = Mycielskian G;
   consider D being finite Clique of MG such that
A3: order D = clique# MG by Def15;
   clique# G <= clique# MG by Th84,Th58;
   then clique# G < clique# MG by A2,XXREAL_0:1;
  hence contradiction by A1,A3,Th109;
end;
