Questions tagged [theorem-proving]
The theorem-proving tag has no usage guidance.
19
questions
1
vote
0answers
52 views
Can Mathematica be used as a proof assistant?
Mathematica have an extensive gallery of mathematical results, as well as a strong rule-based deduction system. Since v12.*, automated proving features have been added to it too.
I believe for ...
0
votes
0answers
21 views
Clarifying the syntax of FindEquationalProof
Could someone clarify the definitions of "statement" and "expression" in the manual entry for FindEquationalProof?
The best I can make of it is that an expression $E$ is either a ...
1
vote
0answers
48 views
Axiomatizing naturals
Trying to implement the naturals in Mathematica, I follow E. Mendelson, Introduction to Mathematical Logic, Ch. 3, Par. 1.
Here is my code for the axioms (exept the induction axiom)
...
2
votes
1answer
76 views
How to deduce circle theorems in Wolfram language?
I can deduce the first one by applying FindGeometricConjectures on the following scene:
...
-2
votes
1answer
122 views
Proving an integral identity [closed]
Assuming $f$ is continus on $[0,\pi]$, show that
$$\int_{0}^{\pi }xf(\sin x)dx=\frac{\pi }{2}\int_{0}^{\pi }f(\sin x)dx$$
I tried to demonstrate it using integration by parts, but I did not succeed.
...
1
vote
1answer
73 views
Counting real roots of bivariate polynomial
For a proof, I'm working with a polynomial $p(x,m)$ and I need to show that: For any $m\in (0,6)$, $p_m(x)\equiv p(x,m)$ has a unique real root in $(0,1/2)$. I find that this is true by using Reduce ...
2
votes
0answers
66 views
Natural deduction with FindEquationalProof
Out of curiosity, I'm trying to implement a natural deduction prover in Mathematica using FindEquationalProof. So far, I've implemented a few of the easier rules:
<...
7
votes
1answer
181 views
Using logical equivalence to prove PL statements
I'm trying to use those Logical equivalence as axioms to prove some PL statements,
In this case I followed the examples in the documentation that didn't use the build-in logic functions$\{\text{And}[,]...
6
votes
3answers
442 views
Basic theorem proving in Mathematica?
Let's say we have the following:
p is prime
n > 1 (n is an integer)
p = nq (I.e. p is a multiple of n)
It can be proved that ...
5
votes
1answer
99 views
FindEquationalProof to prove divisor theorem
I'm trying to implement proofs of concepts for Equational Proofs on some basic number theory theorems.
One such example is:
"let a and b be positive integers and let d = gcd (a, b). If t divides ...
0
votes
1answer
239 views
Implicit Function Theorem
I think I am stuck here right now:
The exercise is to use implicit differentiation to determine y' considering the following equation:
I managed to do this with:
...
4
votes
0answers
70 views
Four color theorem in Mathematica [closed]
The four color theorem is a theorem about graphs (as in graphs and networks) and it was proved with the aid of a computer. To date, there is no hand-checkable proof. The software that was used to ...
1
vote
0answers
88 views
FindEquationalProof with implications
Motivated by this question in mathematics, my Mathematica question is essentially this one, but alas the answer to that isn't quite adequate. I'm not interested in verifying that a proof is valid or ...
6
votes
1answer
262 views
FindEquationalProof with Logic in Wolfram Mathematica
I try to "make" proof in Wolfram Mathematica.
Thats a proof:
if a->b and b->c then a->c
I tried
...
6
votes
3answers
262 views
Why Can't Mathematica Resolve this Simple Quantified Expression?
I've been using Mathematica as a hobbyist, off and on, for some time. So while I'm by no means an expert I've used it long enough to know that what might seem obvious to me is not necessarily obvious ...
5
votes
1answer
184 views
Implementing the field axioms with FindEquationalProof?
I am fiddling around with FindEquationalProof, currently trying to prove some basic statements for fields. I have a set of axioms which almost constitutes the field theory axioms:
...
9
votes
1answer
170 views
Proving uniqueness of group identity element
Start, as in the Mathematica 11.3 documentation, with:
...
10
votes
2answers
222 views
Clues on theorem proving tools?
I'm trying to prove $[a \cup (b \cap c ) = (a\cup b)\cap (a\cup c)]$ with Mathematica. But I don't know what function I should use. I've rewritten the sentence in the following way:
...
10
votes
4answers
2k views
How can I calculate the limit without using L'Hôpital's rule
I need to prove this limit without using L'Hôpital's rule:
$$\lim_{x\to 0} \frac{(1+a\,x)^{1/4} - (1+b\,x)^{1/4}}{x} = \frac{a-b}{4}$$
How can I do it in Mathematica?