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How to express in a diplomatic, but not faint way that an old (and popular) notion should be dismissed in favor of a new (and better) one?

I'm comparing two (mathematical) notions, say 'functoid' and 'punctoid' (these are fictitious names for the sake of discussion), and I'm arguing that punctoids should be definitely preferred to functoids for a series of reasons.

To convey this idea, I would like to use an expression, which is neither too strong nor too faint. I have thought of something like the following:

In a way, what we have just remarked makes the notion of functoid à la Craig and Daniel overruled by punctoids.

But I'm not sure about my use of the term 'overruled'. I had also thought of replacing it with 'shelved', but this sounds too mild to my ears.

Any suggestion?