رَأَيْتُ مُعَلِّمِي الْمَدْرَسَةِ.
Translation: I saw the teachers of the school.
رَأَيْتُ: past verb with subject tāʾ; مُعَلِّمِي: accusative object with yāʾ, muḍāf with the nūn removed; الْمَدْرَسَةِ: genitive complement with kasra.
سَلَّمْتُ عَلَى مُعَلِّمِي الْمَدْرَسَةِ.
Translation: I greeted the teachers of the school.
سَلَّمْتُ: past verb with subject tāʾ; عَلَى: preposition; مُعَلِّمِي: genitive with yāʾ, muḍāf with nūn removed; الْمَدْرَسَةِ: genitive complement.
Rule: Iḍāfa deletes nūn; the governing expression determines accusative or genitive.