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I'm trying to become better with using proper terminologies and standard notation when taking notes, which lead me to think:

Similar to the indication of a completed proof by use of the Q.E.D. mark, or "∎", is there a standard method as to indicate the end of a simplified definition?

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    $\begingroup$ What do you mean by "simplified definition"? $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented Mar 24, 2020 at 16:59
  • $\begingroup$ QED "quod erat demonstrandum", literally meaning "what was to be shown", doesn't fit, but I see no problem with the box sign. An alternative is (using 'theoremstyle" in latex) to use italics in the definition environment. I guess anyway that the most standard marking is the blank line, which is automatic after definition environment. $\endgroup$
    – YCor
    Commented Mar 24, 2020 at 16:59
  • $\begingroup$ I concur with @Carl-FredrikNybergBrodda: it would help to know just what you mean here. If you have a definition and then it gets simplified, perhaps in several steps to equivalent but shorter forms, then I would do this: Don’t give the definition first, but rather prove the lemma that the various descriptions of the phenomenon are equivalent, and then define: A (blah) that satisfies any one of the conditions of the above Lemma will be said to be (wudge). $\endgroup$
    – Lubin
    Commented Mar 24, 2020 at 21:46

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Following Euclid, you could use QEF (quod erat faciendum – which had to be done). Euclid used the Greek version of this (ὅπερ ἔδει ποιῆσαι) to close propositions that were not proofs of theorems, but constructions of geometric objects.

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  • $\begingroup$ What if I'm not presenting the constructions? I could be interpreting the use of QEF wrong; I'm questioning whether or not I'm able to use QEF due the sake of my simplification being for ease of notation, despite the unsimplified definition being usable. $\endgroup$
    – Seligmann
    Commented Mar 24, 2020 at 17:11

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