
theorem Th102:
for G being SimpleGraph, x, y being set
 st {x, y} in Edges G holds {[x,union G], y} in Mycielskian G
proof
  let G be SimpleGraph;
  set uG = union G;
  let x, y be set;
A1: { {xx,[yy,uG]} where xx, yy is Element of uG : {xx,yy} in Edges G }
       c= Mycielskian G by MYCIELSK:3;
  assume A2: {x, y} in Edges G;
   then x in uG & y in uG by Th13;
   then {[x,uG], y} in
     { {xx,[yy,uG]} where xx, yy is Element of uG : {xx,yy} in Edges G } by A2;
  hence {[x,union G], y} in Mycielskian G by A1;
end;
