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February 8th, 2019, 10:03 AM  #1 
Newbie Joined: Feb 2019 From: Israel Posts: 16 Thanks: 0 Math Focus: general topology  A lemma which is a special case of a theorem
It is often the case that a theorem is called using a lemma which in turn is an easy consequence of the theorem (in other words, is a special case of the theorem). Which term could you suggest specifically for such a lemma? I think about using my own coined word (like "specialia") to denote such lemmas in my book. Is it worth to coin a new word? 
February 8th, 2019, 10:23 AM  #2  
Senior Member Joined: Aug 2012 Posts: 2,259 Thanks: 686  Quote:
A lemma is a minor theorem that helps you prove a major theorem. In written presentations, corollaries come after their corresponding theorem; and lemmas come before the theorem they're helping to prove  
February 8th, 2019, 10:25 AM  #3  
Newbie Joined: Feb 2019 From: Israel Posts: 16 Thanks: 0 Math Focus: general topology  Quote:
 
February 8th, 2019, 12:39 PM  #4  
Newbie Joined: Feb 2019 From: Israel Posts: 16 Thanks: 0 Math Focus: general topology  Quote:
 
February 8th, 2019, 02:32 PM  #5 
Senior Member Joined: Dec 2015 From: iPhone Posts: 480 Thanks: 73 
Call them “tip” or “hint” .

February 8th, 2019, 02:33 PM  #6  
Senior Member Joined: Aug 2012 Posts: 2,259 Thanks: 686  Quote:
But a theorem is generally not an easy consequence of a lemma. Rather, a lemma is kind of a building block. It's something you need to prove along the way to the main theorem; but it's selfcontained enough that you can pull it out. Sometimes because you want to use it for something else; or because it simplifies the narrative flow of the main theorem. It's sort of like the programming practice of pulling out a chunk of code into its own subroutine. You're right, a lemma need not make the main theorem easy. But really it's just terminology, these aren't meaningful distinctions, as the axiom of choice, Zorn's lemma, and the wellordering theorem show. A lot of the naming is historical accident.  

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case, lemma, special, theorem, writing advice, writing style 
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