From: Rabbi Akiva Eiger
To: Unknown recipient
Rabbi Akiva Eiger addresses his nephew's proposed resolution to the Sha'agas Aryeh's question of why the Chachamim did not challenge Rabbi Yehudah's kal vachomer requiring chametz to be burned by invoking the sofo lehakeil argument of permitted ashes. Rabbi Akiva Eiger introduces a fundamental distinction: hee hanosenes (a logical-reversal argument invalidating a kal vachomer) only applies when the leniency exists independently of the stringency; when the leniency cannot exist without the stringency being present in the same scenario, hee hanosenes does not apply. Since permitted ashes can only result from burning having taken place, the leniency is structurally inseparable from the stringency, and therefore the Chachamim could not invoke sofo lehakeil regarding ashes.
Source: Shu"t Rabbi Akiva Eiger §188