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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A Paradox in graph theory?
I was reading minimum spanning trees in CLRS and came across the following corollary which is basis of algorithms to compute minimum spanning tree:
Corollary 23.2
Let G = (V,E) be a connected, undirected graph with a real-valued weight function w…
user4952610
3
votes
2 answers
Proof: Check if two integer arrays are permutations of each other using linear time and constant space
I was interested in creating a simple array problem with running time and space constraints. It seems that I have found a solution to my problem. Please read the initial description comment of the problem in the following java code:
/*
* Problem:…
ljeabmreosn
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Prove that f(n) = Θ(g(n)) iff g(n) = Θ(f(n))
I have been given the problem:
f(n) are asymptotically positive functions. Prove f(n) = Θ(g(n)) iff g(n) = Θ(f(n)).
Everything I have found points to this statement being invalid. For example an answer I've come across states:
f(n) = O(g(n))…
user3068177
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Proof with false hypothesis in Isabelle/HOL Isar
I am trying to prove a lemma which in a certain part has a false hypothesis. In Coq I used to write "congruence" and it would get rid of the goal. However, I am not sure how to proceed in Isabelle Isar. I am trying to prove a lemma about my le…
Martin Copes
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Not equal succesors in Coq
I am trying to prove the following lemma in Coq:
Lemma not_eq_S2: forall m n, S m <> S n -> m <> n.
It seems easy but I do not find how to finish the proof. Can anybody help me please?
Thank you.
Martin Copes
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Prove Logical Operations Using Inference Rules
Premise 1: p ∧ q
Premise 2: q → r
Premise 3: s → ¬r
Premise 4: ¬r → ¬u
Premise 5: t ∨ s
Premise 6: t → ¬p ∨ U
Prove: u ∧ q
Does anybody know how to solve this proof using rules of inference? I know the rules of inference like modus ponens/tollens…
user4780686
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Prove that one hypothesis is negation of another in Coq
For example I have these two hypotheses (one is negation of other)
H : forall e : R, e > 0 -> exists p : X, B e x p -> ~ F p
H0 : exists e : R, e > 0 -> forall p : X, B e x p -> F p
And goal
False
How to prove it?
Valery Tolstov
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Termination implies existence of normal form
I would like to prove that termination implies existence of normal form. These are my definitions:
Section Forms.
Require Import Classical_Prop.
Require Import Classical_Pred_Type.
Context {A : Type}
Variable R : A -> A -> Prop.
…
N F
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Seeming contradiction typechecks in Idris
I have the following definition of a predicate on vectors that identifies if one is a set (has no repeated elements) or not. I define membership with a type-level boolean:
import Data.Vect
%default total
data ElemBool : Eq t => t -> Vect n t ->…
gonzaw
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Proving identity for binary operator on Fin
I've defined an operator, +- (ignore the terrible name), as follows:
infixr 10 +-
(+-) : Fin (S n) -> Fin (S m) -> Fin (S (n + m))
(+-) {n} {m} FZ f' = rewrite plusCommutative n m in weakenN n f'
(+-) {n = S n} (FS f) f' = FS (f +- f')
The…
j11c
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Proving to Agda that we're talking about the same thing
I'm trying to prove a contradiction, but I run into an issue trying to prove to Agda that the sigma domain type returned by the <>-wt-inv is the same sigma as seen earlier in the proof.
I expect that the uniq-type proof should help me there, but I…
A.J.Rouvoet
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How do you prove probabilities are closed under multiplication with dependent types?
I'm working a bit with Idris and I've written a type for probabilities - Floats between 0.0 and 1.0:
data Probability : Type where
MkProbability : (x : Float) -> ((x >= 0.0) && (x <= 1.0) = True) -> Probability
I want to be able to multiply…
Jack
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Idris proof by definition
I can write the function
powApply : Nat -> (a -> a) -> a -> a
powApply Z f = id
powApply (S k) f = f . powApply k f
and prove trivially:
powApplyZero : (f : _) -> (x : _) -> powApp Z f x = x
powApplyZero f x = Refl
So far, so good. Now, I try to…
mudri
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How to prove that Greedy approaches will not work
For any given problem where greedy approaches will not give optimal value, we can find a counter example to disprove that approach.
However, is it possible to prove that for a given problem, any greedy approach in general will not work.
Shamim Hafiz - MSFT
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Proof of code execution
Is there a way to prove, I mean technically and legally prove, that a piece of code has been ran at a certain time on a computer ?
I think this could be achieved by involving cryptographic techniques like checksums and trusted timestamps, what do…
Silas
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