
theorem Th36:
for  x being set holds CompleteSGraph {x} = {{},{x}}
proof
 let x be set;
 thus CompleteSGraph {x} c= {{},{x}} proof
  let a be object;
  assume a in CompleteSGraph {x};
   then consider V being finite Subset of {x} such that
  A1: a = V and card V <= 2;
     a = {} or a = {x} by A1,ZFMISC_1:33;
   hence thesis by TARSKI:def 2;
 end;
A2: {x} = Vertices CompleteSGraph {x} by Lm1;
A3: x in {x} by TARSKI:def 1;
 thus {{},{x}} c= CompleteSGraph {x} proof
   let a be object;
   assume a in {{},{x}};
   then a = {} or a = {x} by TARSKI:def 2;
   hence thesis by A2,A3,Th20,Th24;
 end;
end;
