
theorem Th100:
for G being SimpleGraph, x, y being set
 st {[x,union G], y} in Mycielskian G holds x <> y
proof
  let G be SimpleGraph, x, y be set;
  set MG = Mycielskian G; set uG = union G;
  assume A1: {[x,uG], y} in MG;
  assume A2: x = y;
  then [x,uG] <> y by Th3;
  then {[x,uG], y} in Edges MG by A1,Th12;
  hence thesis by A2,Th99;
end;
