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The prohibition on Shabbos of Mechamer (guiding an animal) is not punishable with Kares.
When a parent instructs his son, who is a Kohen, to enter a cemetery, or instructs a child to avoid returning a lost object, the child shall not obey his parent. (1)
One may not build the Beis ha'Mikdash on Shabbos. (2)
The awe a person must have in the Beis ha'Mikdash is not of the Beis ha'Mikdash itself but rather fear of He Whose Presence resides in the Beis ha'Mikdash. (3)
A person expresses fear of the Beis ha'Mikdash by refraining from entering Har ha'Bayis with his staff, shoes, money belt, or the dust on his feet. He also may not use it for a shortcut, and certainly he may not spit there. (4)
Rebbi Yosi: The Melachah of igniting a fire is punishable only with Malkus and not with Kares. Rebbi Nasan: It is punishable with Kares. (5)
A Mitzvah that is a physical obligation applies both in Eretz Yisrael and in Chutz la'Aretz.
Our Sages derive from a Kal va'Chomer that Beis Din may not be Mechalel Shabbos for the purpose of putting an evildoer to death.
Death by Sereifah entails cooking a piece of lead, which is no different from cooking the ingredients of the dyes that were used for the Mishkan.
A BIT MORE
1. This is because both the parent and child are obligated to honor Hashem.
2. Even though it is a Mitzvas Aseh to build the Beis ha'Mikdash, the Mitzvas Aseh does not override the prohibition against performing Melachah on Shabbos.
3. Just as a person does not fear the Shabbos, but rather his fear is of the One Who commanded the Mitzvah of Shabbos, similarly the fear that one must have while in the Beis ha'Mikdash is of the One Who commanded the Mitzvah of the Beis ha'Mikdash.
4. These regulations apply even after the destruction of the Beis ha'Mikdash. Our Sages derive from Shabbos that just as the Mitzvah of Shabbos applies at all times, the Mitzvah of fearing the Beis ha'Mikdash applies always.
5. Rebbi Nasan maintains that the reason why the Torah states the prohibition against igniting a fire as a separate prohibition is not to teach that it is not punished with Kares, but rather to teach that a person is obligated to bring a Korban Chatas even if he does only one Melachah b'Shogeg.
A FATHER WHO INSTRUCTS HIS SON TO TRANSGRESS THE TORAH
The Beraisa says that a child shall obey a parent who instructs him to transgress the Torah. The Shitah Mekubetzes asks that a father who instructs his child to transgress the Torah is not following the proper path, and there is no Mitzvah to honor such a father anyway. The Shitah Mekubetzes answers that if the concept of Aseh Docheh Lo Sa'aseh would apply and the Mitzvah of Kibud Av would override the Torah prohibition, then the father would be doing nothing wrong by instructing his son to transgress the Torah prohibition, since the son would be obligated by the Torah to listen to the father and to ignore the Torah prohibition.
USING A SYNAGOGUE AS A SHORTCUT
If a synagogue has two entrances, one may not go enter one entrance and exit the other with intent to use the synagogue as a shortcut. If a shortcut exited there prior to the building of the synagogue, then it is permitted to use the synagogue as a shortcut. If one did not enter with intent to use it as a shortcut, he may exit from the second entrance. It is a Mitzvah for one who enters the synagogue for Tefilah to exit from the second entrance. (Shulchan Aruch OC 151:4)
The prohibition against using a synagogue for a shortcut is because it is prohibited to enter a synagogue for a purpose other than a Mitzvah.
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