zechiras yetzi'as Mitzrayim - zman gerama

My son is such a R’ Ovadya Yosef admirer that he bought one of the new biographies (this is the only gadol biography I think he owns) called Abir HaRo’im that came out after R’ Ovadya’s passing.  In a footnote towards the end of the book there is a story about a meeting that took place on Pesach between R’ Ovadya and another Rav whose name I apologize for not remembering (the truth is that I am not familiar with many of the names of talmidei chachamim mentioned in the book due to my ignorance of the sefardi world).  In the Torah discussion that took place between them, R’ Ovadya asked why we need the derashos of “ymei chayecha – l’rabos ha’yamim” and “kol – l’rabos ha’laylos” that we are familiar with from the haggadah shel Pesach.  Why could the pasuk not simply have said “l’ma’an tizkor… b’chayecha,” and we would assume (why not?) the mitzvah of zecheiras yetzi’as Mitzrayim applies 24x7? 

The talmid chacham who R’ Ovadya was speaking to answered by pointing to the Sha’agas Aryeh’s chiddush that even though zechiras yetzi’as Mitzrayim applies both by day and at night, it is still classified as a mitzvas aseh she’hazman gerama because the mitzvah done by day is an independent chiyuv from that done at night.  In reality, there are two separate kiyumim that apply in two distinct time periods that happen to run concurrently.  Based on this, we understand why the pasuk uses two derashos.  Had the pasuk said “l’ma’an tizkor… b’chayecha,” it would imply that there is one mitzvah that applies 24x7.  By giving us a derasha to teach us the mitzvah during the day and a separate derasha for the mitzvah at night, the pasuk teaches that they are in fact two separate kiyumim and the mitzvah is zman gerama.  (R’ Ovadya apparently got a lot of simcha from the teirtuz – as I hope you do too.)