Learn English – How to express in a diplomatic, but not too subtle, 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 that is neither too strong nor too subtle. I have been thinking about 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 soft to my ears. Please note that I need to stick to a formal register, as this is intended for a publication.

Any suggestions?

Best Answer

supersede, as defined by Dictionary.com

to set aside or cause to be set aside as void, useless, or obsolete, usually in favor of something mentioned; make obsolete: They superseded the old statute with a new one.

Steven Weinberg (Nobel Prize winner in Physics, 1979) used supersede in this way in his book Lectures on Quantum Mechanics, page 21:

It was hopeless to use matrix mechanics to solve more complicated problems, like the hydrogen molecule, so wave mechanics largely superseded matrix mechanixs among the tools of theoretical physics.

The OP's sentence thus becomes:

In a way, what we have just remarked makes the notion of functoid à la Craig and Daniel superseded by punctoids.

I suggest rewriting the sentence to say:

In a way, what we have just remarked means that punctiods supersede the notion of functoids a la Craig and Daniel.

Footnote about the use of a la in a math article: See Using the Mathematics Literature.