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I want to say "By assuming XXX, it makes the proof of most theorems (become) trivial and less interesting"

Should I use "become" here? It looks to me both of them is ok...

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You don't need or even want become in this sentence. Make in constructions like MAKE X Y has the meaning cause X to become Y, so become is superfluous.

You also want to delete by and it, or rewrite to justify the by. That by clause wants an implicit subject who does the assuming. It won't work, because it 'stands for' the clause itself. For instance, you could write

By assuming XXX, we make the proof &c

But it is much simpler to make assuming XXX the 'agent' which causes the proof to become trivial:

Assuming XXX makes the proof &c

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