12
votes
3answers
449 views

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 ...
3
votes
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 ...
39
votes
9answers
4k views

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 ...
5
votes
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 ?
5
votes
6answers
2k views

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 ...
22
votes
5answers
2k views

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 ...
11
votes
7answers
1k views

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)