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0
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1answer
642 views

Is there any danger far from home? (Edited & Revised Version) [closed]

The notion of formal proof is defined by finite sequences ($<\omega$ - sequences) of sentences. In some sense if a sentence $\sigma$ is (finitely) provable from the theory $T$ it is very "near" to ...
2
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1answer
155 views

Proof of regularity for bounded elliptic problem

We consider the boundary value problem for potential in the form: $$-\Delta u(\boldsymbol{x})=0,\quad \boldsymbol{x}\in \mathbb R^3\smallsetminus S,$$ with boundary conditions $$\nabla ...
2
votes
1answer
357 views

Hilbert style axiomatic proof or sequent Calculus?

I am puzzling with the question which of the two proof systems (Hilbert style axiomatic proofs or substructural Sequent Calculi) is the most discriminatory? With discriminatory I mean is which proof ...
2
votes
1answer
915 views

Where is a proof of “2 is more than 1 plus 1” said by Saunders Mac Lane? [closed]

I came across this statement in the autobiography by Saunders Mac Lane. It was the interaction between solenoids and group extension that got our collaboration started, and this first work of ...
1
vote
1answer
299 views

Since an inconsistent system can prove its own consistency…

Say a proof for the consistency of a formal system (proved within the formal system) is known. There are two possible cases: 1. the formal system is consistent and it can be and has been proven to be, ...
2
votes
1answer
277 views

Sequent calculus: is there a complete linear reasoning (i.e., no trees)?

In Gentzen's sequent calculus, a formal proof is described by a tree, with each node representing the sequent obtained from the child(ren) by applying a given inference rule. If no inference rule has ...
15
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3answers
780 views

Finite versions of Godel' s incompleteness

Assume you have some notion of proof complexity: for instance, at the basic level, the length of a proof, or the number of symbols used, take your pick (there are more involved measures, but for sake ...
1
vote
0answers
337 views

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 ...
8
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1answer
385 views

Proving that a combinatorial sequence has no compact formula

Suppose we have a sequence $a_n$ given by some combinatorial formula, e.g. involving a sum of n terms (like ${n \choose k}^{10}3^{-k}$ etc.). Sometimes it is plausible that there is no compact ...
10
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2answers
2k views

Consequences of technically proving anything in Coq (on at least Linux) exploiting a bug? [closed]

Technically, it is possible to prove anything in Coq proof assistant [1] (on at least Linux) due to a programming feature (or bug). This seems tractable when validating large proofs. Human analysis ...
15
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4answers
3k views

How true are theorems proved by Coq?

Less tongue in cheek, is it known what the relative consistency is for theorems proved with an automatic theorem prover? Of course this depends somewhat on what assumptions one makes with respect to ...