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I saw a lot of usage of machinery, mechanism, to be used with similar meaning as techniques, ways, methods,....

For example, my math teacher said the machinery in the proof of some theorem is not heavy. Mechanism is also used to describe how something works.

I have actually been confused if they can mostly be exchangeable.

Also are there similar terms that can be used in this kind of scenario?

PS: I have asked similar questions before here, but the post got closed. cerberus encouraged me to ask again.

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up vote 2 down vote accepted

For example, my math teacher said the machinery in the proof of some theorem is not heavy.

Your math teacher was employing a metaphor. He was not referring to literal machinery.

You might be looking for one of the synonyms of procedure:

procedure noun course of action, plan of action, action plan, policy, series of steps, method, system, strategy, way, approach, formula, mechanism, methodology, modus operandi, MO, technique; routine, drill, practice, operation.

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