LessonsIsm Inna and the Noun Governed by Lā of Generic NegationQuiz

وَإِنْ كَانَ مَعْرِفَةً أَوْ نَكِرَةً مَفْصُولًا بَيْنَهُ وَبَيْنَ «لَا»، كَانَ مَرْفُوعًا، وَيَجِبُ تَكْرِيرُ «لَا» مَعَ اسْمٍ آخَرَ.
Translation: If the noun is definite, or is indefinite but separated from lā, it is nominative, and lā must be repeated with another noun in this construction.

The source says that when the noun is definite, the special lā construction does not operate: the noun is nominative, and lā is repeated with another noun.
In «لَا زَيْدٌ فِي الدَّارِ وَلَا عَمْرٌو», Zayd is a proper name, so the nominative form is used.

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If the Noun Is Definite

Ism Inna and the Noun Governed by Lā of Generic Negation

وَإِنْ كَانَ مَعْرِفَةً أَوْ نَكِرَةً مَفْصُولًا بَيْنَهُ وَبَيْنَ «لَا»، كَانَ مَرْفُوعًا، وَيَجِبُ تَكْرِيرُ «لَا» مَعَ اسْمٍ آخَرَ.
Translation: If the noun is definite, or is indefinite but separated from lā, it is nominative, and lā must be repeated with another noun in this construction.

The source says that when the noun is definite, the special lā construction does not operate: the noun is nominative, and lā is repeated with another noun.
In «لَا زَيْدٌ فِي الدَّارِ وَلَا عَمْرٌو», Zayd is a proper name, so the nominative form is used.