How to properly express that a proof of a proposition verifies a similar one simply by exchanging $\cap$s and $\cup$s?

Asked Oct 20 '19 at 03:56

Active Oct 20 '19 at 04:05

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I want to write a proof for two similar propositions, both proofs are similar except that all the $\cap$s in the first proof are replaced with $\cup$s respectively. How can I write formally and clearly, I mean, like a native-speaker, and avoid the repetition?

I write the following sentence in the last part of my proof.

The latter one is similar to the previous one, except replacing $\cap$s with $\cup$s.

Is this a readable proof for you? Or how can I modify this?

edited Oct 20 '19 at 04:05

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asked Oct 20 '19 at 03:56

闫嘉琦

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Yes, this is readable and perfectly comme-il-faut. (Assuming, of course, that the analogy indeed holds up.) – darij grinberg Oct 20 '19 at 04:02
@darijgrinberg Thanks alot. – 闫嘉琦 Oct 20 '19 at 14:29

How to properly express that a proof of a proposition verifies a similar one simply by exchanging $\cap$s and $\cup$s?

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