
theorem Th39:
for G being SimpleGraph, x being set st x in Vertices G
  holds CompleteSGraph {x} c= G
proof
 let G be SimpleGraph, x be set such that
A1: x in Vertices G;
A2: CompleteSGraph {x} = { {}, {x} } by Th36;
A3: {} in G by Th20;
A4: {x} in G by A1,Th24;
  thus CompleteSGraph {x} c= G by A2,A3,A4,ZFMISC_1:32;
end;
