Erlkönig: Study versus Fail - a Proof

Given: Study = No Fail
And: No Study = Fail

1. Study + No Study = Fail + No Fail

2. Study ( 1 + No ) = Fail ( 1 + No )

3. Study ( 1 + No ) = Fail ( 1 + No )
          --------         ----------
         ( 1 + No )        ( 1 + No )

Q.E.D. Study = Fail

...(*stares at Study Guide*).... Curse You