وَبَدَلُ الِاشْتِمَالِ: وَهُوَ مَا مَدْلُولُهُ مُتَعَلِّقُ الْمَتْبُوعِ، نَحْوُ: «سُلِبَ زَيْدٌ ثَوْبُهُ».
Translation: Badal of ishtimāl denotes something associated with the antecedent; for example, Zayd was robbed of his garment.
The author says related to the antecedent, not part of the antecedent. Clothing is associated with Zayd but is not a bodily part. That is the core distinction from part-for-whole badal.