I found this sentence in Tofugu's workbook.
My question is: Why is the る not dropped so it becomes 見に, as in this sentence:
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Because it's 見るには and not verb + に + いく。They're completely different things. Verb + には is it's own thing. It means like 'in order to x / to accomplish x'. This is something that is extremely unintuitive at first but it makes a bit more sense when you think about how には is used with regards to physical objects. には is used to indicate that something is inside something else or that something is placed in a physical location. So for example 「この箱にはおもちゃがある」"There are toys in this box". So, how does it apply to verbs? Well.. this explanation might not make a lot of sense but if you kind of think of it like 'in order to embody this action (that is, to be inside the action, living it,physically performing it) you need to do X. Is kind of the gist of it.