A proof assistant is software used for creating and checking formal proofs; examples include Coq and HOL. Not to be used for requesting assistance on finding proofs.

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Function extensionality: does it make a difference? why would one keep it out of the axioms?

Yesterday I was shocked to discover that function extensionality (the statement that if two functions $f$ and $g$ on the same domain satisfy $f\left(x\right) = g\left(x\right)$ for all $x$ in the ...
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1answer
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Wanted: a “Coq for the working mathematician”

Sorry for a possibly off-topic question -- there are four StackExchange subs each of which could be construed as the proper place for this question, and I've just picked the one I'm most familiar ...
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29answers
725 views

Formalizations of category theory in proof assistants

What are the existing formalizations of category theory in proof assistants? I'm primarily interested in public-domain code implementing category theory in a proof assistant (Coq, Agda, ...
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2answers
797 views

At which level is it currently possible to write formal proofs?

I am wondering whether I should try to have some fun using proof systems. I have never used such a system, but I have some experiences in logic and programming. My question is: At which level of ...
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0answers
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Beatty proof adaptation ?

If $m$ and $n$ are coprime integers, prove that each of these $m+n-2$ fractions: $$\frac{m+n}{m},\frac{2(m+n)}{m},\frac{3(m+n)}{m},...,\frac{(m-1)(m+n)}{m},$$ ...
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1answer
199 views

prod and sig in COQ

Hello, Apparently in COQ the type prod (with one constructor pair) corresponds to cartesian product and the type sig (with one constructor exist) to dependent sum but how is described the fact that ...
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0answers
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Can someone help me in a proof about Kolakoski sequence? [closed]

Hello everyone. I am not a mathematician but recently I was thinking about one of Kimberling's questions he posted here: http://faculty.evansville.edu/ck6/integer/index.html , i.e the question I asked ...
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2answers
447 views

How to interpret conflicting formal proofs about “a mod 0 = ? ”

The proof assistants Coq and Isabelle give conflicting formal proofs about $a \mod 0 \qquad \forall a \in \mathbb{Z}$. According to Coq $$ a \mod 0 = 0$$ and Isabelle proves $$ a \mod = a$$ ...
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Why should I trust Coq when assumption-free proof of False in Coq exists? [closed]

Damien Pous announced code for assumption-free proof of False in Coq which means inconsistency in Coq (without using exploits, lol). Damien is critical of "fully certified decision procedure ...
3
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1answer
874 views

Proving inequalities over algebraic structures

I've been looking at proof techniques in formal systems like Coq and Agda recently, and encountered the newring tactic described here for proving equalities over ...
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4answers
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Why is it so difficult to write complete (computer verifiable) proofs?

For example I have read that is agony to give a complete proof of the Jordan curve theorem. Since all statements are meant to be justified by the postulates, where does the difficulty lie?
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2answers
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What is a semigroup or, what do I do with that associativity proof?

Mathematically, I know what a semigroup is: It is a set S along with an associative binary operation $* : S \times S \rightarrow S$. So far, so good. From a computational perspective, one can ...
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How do they verify a verifier of formalized proofs?

In an unrelated thread Sam Nead intrigued me by mentioning a formalized proof of the Jordan curve theorem. I then found that there are at least two, made on two different systems. This is quite an ...
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1answer
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Is there a known way to formalise notion that certain theorems are essential ones?

Suppose You ask a question beginning from "Why some structure is..." or "Why some object has property..." and several answers arises. Which criteria do You use to qualify which answer is correct? ...
5
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3answers
627 views

Proof formalization

I read some time ago some papers about proof formalization. Typically, I began whith this one, from Lamport. Are there more recent works in this field ?
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6answers
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Is there any proof assistant based on first-order logic?

I'm looking for a proof assistant in order to write formal proofs about basic facts of set theory, such as: $a\subseteq a$ $(a,b)=(c,d)\leftrightarrow a=c\land b=d$ Natural deduction for ...
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5answers
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Proof assistants for mathematics

This question is related to (maybe even the same in intent as) Question 1017, but none of the answers seem to address what I'm looking for. There are a lot of resources available for people who want ...
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7answers
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Intro to automatic theorem proving / logical foundations?

Is there any web-based course or materials about logic / automatic theorem proving? (I checked MIT's OpenCourseWare and I only found a vaguely related AI course)