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
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How to use apply to "extract" a implication in Coq
I'll illustrate using an example.
H : R -> P -> Q
H0 : R
Subgoal:
(Q -> P) \ / (P -> Q)
so my question is how do I extract out (P->Q). I have R already, but when I do
'apply H in H0', it evaluates everything and gives me Q.
some1fromhell
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Why pumping lemma for CFG doesn't work
Language:
{(a^i)(b^j)(c^k)(d^l) : i = 0 or j = k = l}
We take word
w = a^0 b^n c^n d^n
Which obviously belongs to the language because j = k = l
w = uvxyz
|vxy| <= n
|vy| > 1
and now v and y can be:
just a single character and if we pump…
signingPls
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Algorithm Proofs
In this case, f(n), g(n), and h(n) are asymptotically positive functions, which means that there exists an N such that f(n)/g(n)/h(n) > 0, for all n >= N. Given that:
f(n) = Θ(g(n))
g(n) = Θ(h(n))
I need to prove that
f(n=Θ(h(n))).
It is…
user3068177
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Formal verification using denotational semantics?
This might go to cs or cstheory stack exchange, but I have seen the most questions tagged with formal-verification here.
Is there extensive literature on using denotational semantics for program verification?
With a quick search I have…
Gergely
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Given a graph G = (V, E) prove e <= n(n-1)/2 for all n
I'm trying to figure out to solve this problem: Given a graph G = (V, E) prove e <= n(n-1)/2 for all n, where e is the number of edges and n is the number of vertices.
I'm thinking that I should somehow be using math induction to figure out the…
winsticknova
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Prove that p^3 - 1 is a composite number given P > 2
In order to prove a number composite I have to prove that p^3 - 1 = ab
With a and b not being 1 and itself. Its given that p > 2.
I factor it out with differences of squares
p^3 - 1 => (p - 1)(p^2 + p + 1)
And I don't really know what to do next.…
Michael Wu
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3 answers
What's the best way to write Mathematical Proofs on the web?
This question about displaying equations on the web is similar to what I'm asking but does not answer my question. It's about math. I'm extending that to proofs.
This is a key difference because my main difficulty is formatting issues like adding…
tscizzle
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How do I get symbolic square root and logarithm functions in SBV?
The only solution I can find is to do a square root approximation, but this doesn't work symbolically so I can't use it for proving.
Reed Oei
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Cannot rewrite subterm in Coq
I have a proof in Coq where one of the hypothesis is:
H : m = pred q * n + (r + n)
And I have a proven lemma which states:
Lemma suma_conmutativa: forall m, forall n, m + n = n + m.
Where + is Notation for a function called suma that I…
Martin Copes
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2 answers
Minimum spanning tree 2- dimensional graph
This is my home work problem but i dont have any clue how to proceed with this
A “geometric graph” is a special type of graph where the nodes are points on a 2- dimensional
surface and edges are straight lines joining pairs of nodes. Show that the…
kvr
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Proof of existence of prime factorization (Educational)
I am trying to write a proof of the existence of the prime factorization of numbers. It is meant to be educational, so every function is defined, we try not to use Isabelle built in functions. Here is my code:
(* addition*)
primrec suma::"nat ⇒ nat…
Martin Copes
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Proof that these rotation moves can explore the whole binary tree search space
I am working on this project where I am required to find the theoretical proof for following.
I have a particular type of binary trees, where
1) each internal node will definitely have two children.
2) There are n leaf nodes and can be assumed in…
Naman
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Prove n^2 + 5 log(n) = O(n^2)
I am trying to prove that n^2 + 5 log(n) = O(n^2), O representing big-O notation. I am not great with proofs and any help would be appreciated.
Bob Benson
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Does a never claim prove a Linear Temporal Logic formula?
I have an LTL formula, that was automatically generated from a program I used:
(((a))&&F((((b))&&F((c)))))
which reads as
a && F(b && Fc)
I then used the ltl2BA-win.exe program downloaded from here:
LTL 2 BA and got a never claim as…
humbleHacker
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How do I prove that there is a recurrence?
I have the following harmonic sequence:
h(n) = 1 + 1/2 + 1/3 + 1/4 +...+ 1/n
Id like to prove that there's a recurrence with
h(n) (less than or equal to) h( lowerbound( n/2)) + 1
Justin T.
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