Questions tagged [theorem-proving]

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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 ...
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0answers
22 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 ...
3
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1answer
112 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) ...
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1answer
76 views

How to deduce circle theorems in Wolfram language?

I can deduce the first one by applying FindGeometricConjectures on the following scene: ...
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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
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1answer
74 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
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0answers
69 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
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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
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3answers
459 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
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1answer
100 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 ...
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1answer
248 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: ...
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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 ...
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0answers
89 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
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1answer
266 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
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3answers
264 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
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1answer
185 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
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1answer
171 views

Proving uniqueness of group identity element

Start, as in the Mathematica 11.3 documentation, with: ...
10
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2answers
223 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
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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?