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Questions tagged [proof]

A mathematical proof is any mathematical argument which demonstrates the truth of a mathematical statement. Informal proofs are typically rendered in natural language and are held true by consensus; formal proofs are typically rendered symbolically and can be checked mechanically. "Proofs" can be valid or invalid; only the former kind constitutes actual proof, whereas the latter kind usually refers to a flawed attempt at proof.

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How can I prove a type is valid in Agda?

I'm trying to do proofs over dependent functions, and I'm running into a snag. So let's say we have a theorem f-equal f-equal : ∀ {A B} {f : A → B} {x y : A} → x ≡ y → f x ≡ f y f-equal refl = refl I'm trying to prove a more general notion of…
gallabytes
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How to properly use keyword 'theorem' in Isabelle?

I obtained the following code from Isabelle's wikipedia page: theorem sqrt2_not_rational: "sqrt (real 2) ∉ ℚ" proof assume "sqrt (real 2) ∈ ℚ" then obtain m n :: nat where n_nonzero: "n ≠ 0" and sqrt_rat: "¦sqrt (real 2)¦ = real m / real…
Timothy Swan
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Prove that it is undecidable whether a Deterministic LBA accepts an infinite number of inputs

Deterministic Linear Bounded Automaton (LBA) is a single-tape TM that is not allowed to move its head past the right end of the input (but it can read and write on the portion of the tape that originally contained the input). How can I prove that…
Dan Webster
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Using an equivalence in the context to force reduction

The setting for this question is the same "merge of sorted lists" example from this earlier question. {-# OPTIONS --sized-types #-} open import Relation.Binary open import Relation.Binary.PropositionalEquality as P hiding (trans) module…
Roly
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Why CRC 32 Generator is not divisible by 11?

The CRC 32 Generator is a 33 bit bin number: 100000100110000010001110110110111 According to the PDF Page 18, Odd number of bit errors can be detected if C(x) contains the factor (x + 1) CRC 32 should satisfy the property of being able to detect…
Wei Zhong
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Boolean Algebra - Proving Demorgan's Law

I looked all over Google for a boolean algebra (not set theory) proof of DeMorgan's Law, and couldn't find one. Stack Overflow was also lacking in DeMorgan's Law questions. As part of a homework assignment for my CIS 251 class, we were asked to…
Chris Cirefice
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k successive calls to tree successor in bst

Prove that K-successive calls to tree successor takes O(k+h) time. Since each node is visited atmost twice the maximum bound on number of nodes visited must be 2k. The time complexity must be O(k). I dont get where is the factor of O(h) coming. Is…
user2179293
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How can I bind the schematic variable ?case in a rule for proof by cases?

I would like to define a rule for proof by cases, to be used with proof (cases rule: ). I managed to use the case_names and consumes parameters, but I did not manage to bind the schematic variable ?case, so that, inside a case of a proof…
Christoph Lange
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Mathematical proof for a binary tree

I am not hiding this is a part of my homework but I've tried enough before posting here. So... I need to prove for a binary tree that a node k have its left child on 2k and right child on 2k + 1 position. I've proved this with induction. Now I need…
user2147971
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Can someone help me with this proof using the pumping lemma?

I just started reading about the pumping lemma and know how to perform a few proofs, mostly by contradiction. It is only this particular question which I don't seem to find an answer for. I have no idea on how to begin. I can assume that there has…
n00b1990
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Using Omega to prove a lemma in Coq

I am trying to make a proof in Coq using Omega. I spent a lot of time on it, but nothing came to me. I have to say I am new in Coq, so I am not at ease with this kind of language, and I do not have much experience. But I am working on it. Here's the…
Flo
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Proving NP complexity

I'm learning how to prove something is NP. In Thomas Cormen's intro to algorithm book, he states something is NP if given a solution to some problem, you can verify it is correct in polynomial time. Say the problem is 2x + 9 = 55, and let's pretend…
roverred
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Explaining algorithm proofs in plain English

I'm a programmer who never studied Algorithms formally, and have always wanted to fill in that gap in my learning. I'm currently working my way through some books and online material, and I understand conceptually Big O, i.e. what it's for, and the…
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Proving correctness in formal logic

I was wondering if anyone could help me answer this question. It is from a previous exam paper and I could do with knowing the answer ready for this years exam. This question seems so simple that I am getting completely lost, what exactly is it…
Paul Blundell
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Show bit strings with count(1s) = count(0s) isn't regular

Let L be the language consisting of strings over alphabet {0,1} that contain an equal number of 1s and 0s. For example: 000111 10010011 10 1010101010 How can you show that L isn't a regular language?
Andrew Tomazos
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