Originally Posted by Story
Which spells does a Wizard count as "knowing"? For example, Spontaneous Divination allows spontaneously casting divination spells the Wizard knows. Is this any spell in a spellbook the Wizard currently owns? Any spell they've ever learned, even if they lost a spellbook?
This is up to the DM to decide.
The description for wizard spellcasting says that they can "know" any number of spells, but it doesn't elaborate on what spells are treated as "known."
I would personally rule that he only "knows" spells which he is able to prepare. Therefore, if he loses his spellbook, he no longer "knows" the spells contained within it.