תלמוד בבלי מסכת עירובין דף פח/א
אמר רבה בר רב הונא לא שנו אלא למלאות אבל לשפוך אסור
The Gemara in Shabbos (100b and 141a) rules that it is permitted to cause an object to move in a carmelis (כוחו בכרמלית לא גזרו רבנן). Tosafos (here, and to Shabbos 100b d.h. Cocho) finds this ruling in evident contradiction to our Gemara's statements that it is not permitted to spill water from a balcony into the sea because in doing so one causes the water to move more than four amos. Since the sea is a carmelis it seems evident that our Gemara holds that it is forbidden to cause an object to move four amos in a carmelis!? The Tosafos resolve the contradiction by distinguishing between a balcony, which occasionally abuts a reshus ha'rabbim — where, therefore, the Rabbis forbade כוחו בכרמלית — and a boat at sea (the topic of the discussion in Shabbos), which never abuts a reshus ha'rabbim — where, therefore, the Rabbis allow כוחו בכרמלית.
In the final analysis, we see that כוחו בכרמלית is not always permitted. In a novel comparison, R' Shlomo Zalman Auerbach (Teshuvos Minchas Shlomo, Tinyana §33) relates this issue to the question of using a disinfectant that colors the water in a toilet. R' Shlomo Zalman notes that the water that is colored by the initial gush of water upon flushing cannot be considered caused to become colored, but colored by direct action. However, writes R' Shlomo Zalman, even the coloring of the water subsequent to the initial gush, which the person flushing the toilet is only causing, may not be permitted, as we see here that not in all cases do the Rabbis permit causing a prohibited activities — even ones, like moving objects in a carmelis or coloring water, that are at worst rabbinic prohibitions.