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.
Questions tagged [proof]
828 questions
4
votes
1 answer
Why does this SBV code stop before hitting the limit I set?
I have this theorem (not sure if that's the right word), and I want to get all the solutions.
pairCube limit = do
m <- natural exists "m"
n <- natural exists "n"
a <- natural exists "a"
constrain $ m^3 .== n^2
constrain $ m .<…
Reed Oei
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votes
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Proof by case analysis in Coq
I am trying to prove a Proposition about the following function:
Program Fixpoint division (m:nat) (n:nat) {measure m} : nat :=
match lt_nat 0 n with
| false => 0
| true => match leq_nat n m with
| false => 0
| true => S (division…
Martin Copes
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4
votes
2 answers
Well founded recursion in Coq
I am trying to write a function for computing natural division in Coq and I am having some trouble defining it since it is not structural recursion.
My code is:
Inductive N : Set :=
| O : N
| S : N -> N.
Inductive Bool : Set :=
| True : Bool
…
Martin Copes
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3 answers
How would I prove that b = c if (andb b c = orb b c) in coq?
I'm new to coq and I'm trying to prove this...
Theorem andb_eq_orb :
forall (b c : bool),
(andb b c = orb b c) -> (b = c).
Here is my proof, but I get stuck when I get to the goal (false = true -> false = true).
Proof.
intros b c.
induction…
Albtzrly
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4
votes
2 answers
How to understand the time complexity of Kademlia node operation
I'm now learning Kademlia network by reading the classical paper Kademlia: A Peer-to-peer Information System Based on the XOR Metric. I want to understand the complexity of its operation but still cannot figure it out.
In the 3 Sketch of proof…
Justin Yang
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4
votes
2 answers
Using the value of a computed function for a proof in agda
I'm still trying to wrap my head around agda, so I wrote a little tic-tac-toe game Type
data Game : Player -> Vec Square 9 -> Set where
start : Game x ( - ∷ - ∷ - ∷
- ∷ - ∷ - ∷
- ∷ - ∷ - ∷ [] )
xturn : {gs : Vec…
user833970
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4
votes
3 answers
Proving Big-O Sum Rule?
I am unsure how to formally prove the Big O Rule of Sums, i.e.:
f1(n) + f2(n) is O(max(g1(n)),g2(n))
So far, I have supposed the following in my effort:
Let there be two constants c1 and c2 such that c2 > c1. By Big O definition:
f1(n) <= c1g1(n)…
Rome_Leader
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Minimum count of numbers to be inserted in [a,b] such that GCD of 2 consecutive numbers is 1
This question was asked in TopCoder - SRM 577. Given 1 <= a < b <= 1000000, what is the minimum count of numbers to be inserted between a & b such that no two consecutive numbers will share a positive divisor greater than 1.
Example:
a = 2184; b =…
baskar_p
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votes
4 answers
How do people prove the correctness of Computer Vision methods?
I'd like to pose a few abstract questions about computer vision research. I haven't quite been able to answer these questions by searching the web and reading papers.
How does someone know whether a computer vision algorithm is correct?
How do we…
solvingPuzzles
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votes
1 answer
TAOCP Vol 1: Overflowing multiple stacks proof
I am self-studying TAOCP and trying to make sense of the solution to the following problem from Chapter 2.2.2 Linear Lists: Sequential Allocation.
[30] If σ is any sequence of insertions and deletions such as (12), let s0 (σ) be the number of…
Cam Miller
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votes
1 answer
Theorem and Proof Environment in Beamer
I am currently trying to use quarto beamer to making lecture slides. I would like to use the theorem environment in beamer, the qmd file however cannot render properly. Rendering stopped with latex error showing that Command \theorem already…
Ginger Shu-Ying Yeh
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3
votes
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Programmatic proofs for monad laws
In haskell, the users do not have to prove that their monads satisfy the monad laws.
return a >>= k = k a
m >>= return = m
m >>= (\x -> k x >>= h) = (m >>= k) >>= h
If I understand correctly, even if…
Student
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Creating Coq tactic: how to use a newly generated name?
I want to create a Coq tactic that looks something like the following. I assert a proposition named H, I prove that proposition, and then I use simpl within that proposition. The tactic would look something like this:
Tactic Notation "foo" :=
…
Sambo
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3
votes
2 answers
Ada GNATprove insints that 1 is not >= 0
I am trying to prove, that my algorithm for finding second largest value in array works as it should. This is my code:
function FindMax2 (V : Vector) return Integer is
Max : Natural := 0;
SecondMax : Natural := 0;
begin
for I in V'Range…
pucikplay
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3
votes
1 answer
Idris "did not change type" for rewrite with exact same type
Context I'm trying to write a version of ++ for Vect where the compiler can infer the resulting Vect has the expected contents.
Detail I'm struggling to see why this second rewrite isn't working
import Data.Vect
import Data.Nat
infixl 9 ++:
public…
joel
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