On this daf, we discuss the reason why one is permitted to perform a bris on Shabbos, despite the fact that the forbidden melacha of making a wound is an inevitable part of the removal of the foreskin.
We also discuss why it is permitted to perform a bris on someone who has a leprous lesion on the site of the bris.
Various reasons are given for the former, but the most accepted view seems to be that   of Rabbi Yochanan who learns it from the passuk וביום השמיני ימול, (on the eight’s day he shall be circumcised), the derasha being “even on shabbos.”
The later is also derived from a similar דרשה- “בשר אע”פ שיש שם בהרת ” but there is also a view that it is because the positive command of performing a bris pushes aside the negative command of cutting off a leprous lesion,  
This in turn, together with the permission to wear linen tzitzit on a woolen garment or vice versa, seems to serve as examples of  a general rule by which a positive mitzva pushes aside a negative one – עשה דוחה לא תעשה (see the  long sugya in the beginning of Yevamos for a more detailed discussion regarding the source for and parameters of this rule.)
There is, however, another commonly applied rule, which seems to state the complete opposite, and that is the rule of מצוה הבאה בעבירה (A mitzva that comes in/with/from a sin.)
The most famous example of this is found in the Mishna (Sukkah 29b) where we are told that a stolen Lulav is not fit for fulfilling the Mitzva.
Not only does one get punished for stealing the Lulav, but one also does not get the reward for taking the Lulav- not only do the ends NOT justify the means, the means invalidate the end!
Why does one simply not apply the former principle of עשה דוחה לא תעשה  and say that the positive commandment to take the Lulav pushes aside the prohibition of stealing, not only validating the ends (the mitzva of Lulav,) but also the means (stealing it.)
The most obvious distinction can also be found on our daf.
The Gemara is dealing with a case where a person wants to perform service in the Temple but is impure due to a leprous lesion.
It wants to know why the rule of עשה דוחה לא תעשה cannot be applied to allow him to remove the relevant lesion in order to fulfil the mitzva of the divine service.
  Rav Ashi answers that the rule of עשה דוחה לא תעשה only applies when one transgresses the prohibition at the SAME time as one performs the Mitzva.
The logic might be that an action needs to be defined one way or another as either something positive or something negative.
The Chidush (novelty) of this rule is that when ONE action contains both a Mitzva and an aveira, the action is defined as positive, based on the mitzva, rather than negative, based on the aveira.
However, where two separate actions are involved and the prohibition does not take place simultaneously with the mitzva but rather beforehand, like in this case where a person first removes a lesion in order to later be able to perform the service, this reasoning does not apply, and the original prohibition cannot be permitted.
It thus follows from the chiddush of מצוה הבאה בעבירה  that seeing as the original prohibition was not permitted at all, the mitzva that is fulfilled later as a result of the prohibition is also not considered a mitzva at all.
Similarly in our case, seeing as the Lulav is first stolen and only used afterwards for the mitzva, the rule of עשה דוחה לא תעשה  does not apply, and the rule of מצוה הבאה בעבירה  then comes and invalidates even the mitzva.
The problem with this approach is that it could technically be possible to perform the mitzva of lulav at the same time as he steals it.
If one grabs a Lulav from someone on Sukkot and at the same time as  he makes the קנין גזילה   (symbolic act that affects the transaction, in this case giving it the status of a stolen object,) he has intention to fulfil the mitzva of taking it, the rule of עשה דוחה לא תעשה  should surely apply?
Perhaps the answer lies in another rule we have learnt on our daf, namely the reason the Gemara itself has issues with deriving the permission to perform a bris on the site of a leprous lesion: אין עשה דוחה לא תעשה ועשה – a positive commandment can not push aside a prohibition which also involves a positive commandment.
In the case of stealing, there is not only the negative commandment against stealing, there is also the positive command to return whatever one has stolen.
So long as one is still in possession of stolen property, one has not only transgressed the prohibition of stealing, but has avoided the command to return it.
If a person steals a lulav and simultaneously takes it, he is not only transgressing the prohibition of stealing the Lulav- he is also avoiding the Mitzva of returning it.
Thus the rule of עשה דוחה לא תעשה cannot possibly apply, and the rule of מצוה הבאה בעבירה prevents one from fulfilling the Mitzva.
 
In truth, The rule of מצוה הבאה בעבירה also seems to be found in other cases where the prohibition is performed at the same time as the Mitzva.
For example, one who eats מצה של טבל (matza from untithed produce) on Pesach, one  does not fulfill the Mitzva of eating matza, even though the prohibition of eating untithed produce has been performed simultaneously with the mitzva )Pesachim 35a)
However, the Gemara brings a separate passuk to prove this, and although our argument could possibly also be applied to the case of  טבל too, seeing as there is also a positive mitzva to separate the various tithes, we will leave that till Pesachim bli neder.
All this is on the level of technical halachik pilpul.
Yet on an ethical level, the fact that we clearly do not apply the rule of עשה דוחה לא תעשה to stealing, or as far as I am aware, other מצות בין אדם לחבירו can easily be understood.
It is one thing to trade-off one mitzva with another when both are between man and Hashem.
However, if your mitzva will be at the expense of someone else, this goes against the very idea of what mitzvot are supposed to accomplish and is also a tremendous Chillul Hashem.
On such things, Hashem says “”חדשיכם ומועדיכם שנאה נפשי (my soul has hated your new-moons and your festivals- Yeshayahu 1/14/)
Going into the 9 days, this message is more relevant than ever.
These posts are intended to raise issues and stimulate further research and discussion on contemporary topics related to the daf. They are not intended as psak halacha.