Мышь смогла пролезть через узкую щель под дверью.

Questions & Answers about Мышь смогла пролезть через узкую щель под дверью.

Does через always take the Accusative case, and why does щель look like it hasn't changed?
Yes, when через means "through" or "across" a space, it always takes the Accusative case. The word щель (crack/gap) is a feminine noun ending in a soft sign (3rd declension). For these nouns, the Accusative form is identical to the Nominative. We know it is definitely Accusative here because its adjective, узкую (narrow), is in the feminine Accusative form!
How does the prefix про- change the verb лезть in this sentence?
The base verb лезть means "to climb", "to crawl", or "to get into". The prefix про- adds the idea of moving through, past, or squeezing through an obstacle. It is very common to pair verbs starting with про- with the preposition через to really emphasize the action of going through a medium or space.
Why is the verb смогла in the feminine form?
It has to agree with the subject, мышь (mouse). Even though it doesn't end in -а or -я, мышь is a feminine noun. It belongs to the 3rd declension group (feminine nouns ending in a soft sign), which also includes щель (crack) and дверь (door) from this exact same sentence.
Why does it say под дверью (Instrumental) instead of под дверь (Accusative)?
The preposition под (under) takes the Instrumental case when describing a static location, answering the question "where?" (где?). The crack itself is physically located under the door. If the sentence meant the mouse was actively moving to a destination under the door, answering "to where?" (куда?), you would use the Accusative case (под дверь).

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