Describe the conditions under which 'badal al-ishtimal' (بدل الاشتمال) is correctly used in a sentence, providing an illustrative example.

'Badal al-ishtimal' (بدل الاشتمال), or the 'substitute of containing', is a type of 'badal' (بدل - substitute or appositive) in Arabic grammar. A 'badal' is a noun or phrase that renames or explains another noun or phrase, called the 'mubdal minhu' (المبدل منه - the noun being substituted). 'Badal al-ishtimal' occurs when the 'badal' is *related to the 'mubdal minhu' through a quality, characteristic, or some form of connection, but it is not a part of it (like 'badal al-kul' - بدل الكل, the whole for part). The 'badal' *contains or is contained bythe 'mubdal minhu' in some way. The main conditions for using 'badal al-ishtimal' correctly are: First, there must be a clear connection or relationship of containment or association between the 'badal' and the 'mubdal minhu'. Second, the 'badal' must clarify or specify a quality, aspect, or characteristic associated with the 'mubdal minhu'. Third, the 'badal' should not be a physical part of the 'mubdal minhu'; rather, it should be a quality, characteristic, or something related that the 'mubdal minhu' encompasses. Fourth, the 'badal' usually carries a pronoun (الضمير) that refers back to the 'mubdal minhu', solidifying the connection. For example: 'أعجبني زيدٌ علمُه' (a'jabani Zaydun 'ilmuhu) – 'Zayd impressed me, his knowledge.' In this sentence, 'زيد' (Zaydun) is the 'mubdal minhu', and 'علمُه' ('ilmuhu - his knowledge') is the 'badal al-ishtimal'. The knowledge is *associated withor *contained by Zayd, and the pronoun 'ﻪ' ('hu - his') connects the 'badal' back to Zayd. The knowledge isn't a physical part of Zayd, but a quality associated with him that caused the speaker to be impressed. Another example: 'سرق اللص البيت أثاثه' (saraqa al-lisu al-bayta athathahu) – 'The thief stole from the house, its furniture.' Here, 'البيت' (al-bayta - the house) is the 'mubdal minhu', and 'أثاثه' (athathahu – its furniture) is the 'badal al-ishtimal'. The furniture is contained within the house, clarifying *what specifically was affectedby the thief, and the pronoun 'ﻪ' ('hu – its') connects the 'badal' back to the house.