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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Proving a recursive algorithm
I need to prove a recursive algorithm. Normally this would be done using some integer value within the code as the base case for induction like when computing a factorial but with a graph traversal I have no idea where to begin. Here is my…
BlindAsABat
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How to prove x + y - z = x + (y - z) in Coq
I want to prove this :
1 subgoals
x : nat
y : nat
z : nat
______________________________________(1/1)
x + y - z = x + (y - z)
It looks trivial, but it confuse me a lot, and I need it for another proof.
Thanks.
Moody
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Fixed Point and Proof theory
For any given logic program, proof theory of it uses SLD (Selective Linear Definite) resolution to find the satisfiablity of the query. For the same logic program, we can apply fixed point theorem to find the models.
My question is,
should we…
Badri
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An Example from Description Logic Handbook
I dont understand this example very clearly. The example is taken from Description Logic Handbook.
At the last line of the example, "induction is required, hence such reasoning is not first order". That line completely took me off the guard.
your…
Badri
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How to prove the mutual equivalence of peirce, classic, excluded_middle, de_morgan_not_and_not and implies_to_or without using intuition in coq
I simplified the proof procedure of the mutual equivalence of peirce, classic, excluded_middle, de_morgan_not_and_not and implies_to_or primarily written in git@github.com:B-Rich/sf.git as following.
Theorem excluded_middle_irrefutable: forall…
TorosFanny
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Formal Equivalence between programming languages
We have 2 languages which are (informally) semantically equivalent but syntactically different. One is xml and another is script based. How can I go about formally proving that both languages are in fact equivalent. Script approach is just a…
Ketan
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Volume complexities of multihead Turing Machines
I'm trying to prove that for every multihead Turing machine X, there is a multihead Turing machine y such that for any input string z, we have volume(X, z) = Θ(Y(z)) and volume(Y,z) = Θ(Y(z)). In other words, the three values are all equal up to a…
Telo Springs
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Necessary and Sufficient vs Soundness and Completeness
I am trying to learn proof. I came across these 4 terms. I am trying to relate all.
A: X>Y B: Y
user1764183
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How to prove (R -> P) [in the Coq proof assistant]?
How does one prove (R->P) in Coq. I'm a beginner at this and don't know much of this tool. This is what I wrote:
Require Import Classical.
Theorem intro_neg : forall P Q : Prop,(P -> Q /\ ~Q) -> ~P.
Proof.
intros P Q H.
intro HP.
apply H in…
Jaelson Carvalho
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Given a graph G with unique edge weights, are all max spanning trees of G a max bottleneck tree?
The full version of this question is quoted below:
Let G be a connected graph with n vertices, m edges with distinct edge
weights. Let T be a tree of G with n vertices and n-1 edges (i.e. a
spanning tree), and define a bottleneck edge of T to…
Ray
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resolving a clause. Resolved A and B yields
I was wondering why the following resolutions yield true and none rather than (A !D) and (A B C !D):
Resolve (A B C) & (!B !C !D) yields true
Resolve (A B C) & (B C !D) yields none.
user3088470
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How to show that something increases relational expressive power?
How do I show that something increases relational expressive power? For example I have been given a problem in which I need to show whether adding some certain functionality to the select-project-join queries of SQL increases the expressive power.…
optional
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Simple proof of stream of ones in Coq
Taking code from CPDT, I'd like to prove a property for the easy stream ones, which always return 1.
CoFixpoint ones : Stream Z := Cons 1 ones.
Also from CPDT, I use this function to retrieve a list from the stream:
Fixpoint approx A (s:Stream A)…
Olle Härstedt
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Proving a binary tree
How would i go about proving the relationship with j and k if T is a binary tree with k internal vertices and j terminal vertices
In a full binary tee I know that j = k + 1
In a binary tree that is not full I know that j = k if there are an odd…
User9193
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Proving tail-recursive function (calculating powers of an integer)
Here's a function whose corectness I want to prove (written in OCaml):
let rec pow ak a k = if k=0 then ak
else if (k mod 2)=1 then pow (ak*a) (a*a) (k/2)
else pow ak (a*a) (k/2);;
Its specification:
For integers ak, a>0, k>=0 pow returns…
qiubit
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