
theorem :: Sub3b:
for G being SimpleGraph holds G = G SubgraphInducedBy Vertices G
proof
 let G be SimpleGraph;
 thus G c= G SubgraphInducedBy Vertices G proof
   let x be object;
  reconsider xx=x as set by TARSKI:1;
   assume A1: x in G;
   A2: xx c= union G by A1,ZFMISC_1:74;
   thus thesis by A1,A2,XBOOLE_0:def 4;
 end;
 thus thesis;
end;
