# 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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### 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 ...
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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) ...
1answer
76 views

### How to deduce circle theorems in Wolfram language?

I can deduce the first one by applying FindGeometricConjectures on the following scene: ...
1answer
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### 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. ...
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 ...
0answers
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### 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: <...
1answer
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4answers
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### 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?