
theorem Th72:
for G being SimpleGraph, C being Clique of G
  holds Vertices C is StableSet of Complement G
proof
 let G be SimpleGraph, C be Clique of G; set CG = Complement G;
A1: Vertices G = Vertices CG by Lm4;
   reconsider uC = union C as Subset of Vertices CG by A1,ZFMISC_1:77;
    now
      let x, y be set such that
    A2: x <> y and
    A3: x in uC and
    A4: y in uC;
      {x,y} in C by A3,A4,Th53;
      then {x,y} in Edges G by A2,Th12;
     hence {x,y} nin CG by XBOOLE_0:def 5;
    end;
   hence union C is StableSet of Complement G by Def19;
end;
