# Questions tagged [proof-review]

For questions that ask about possible improvements of a working piece of a proof. Make sure to also include the tag for the language used, and follow that tag's guidance regarding additional version-specific tags.

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### Strong induction for nat in Coq

I'm doing some exercises on Coq and trying to prove the strong induction principle for nat: ...
• 195
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### Axiomization of Peano arithmetic in constructive first-order logic

I've been playing with axiomising systems of first-order logic in Coq. I've started to develop the beginning of a framework. As an example I give a minimal phrasing of Peano arithmetic in Coq in the ...
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867 views

### In Lean, contradiction tactic failed but actually goal accomplished

I've been playing with Lean, trying to prove the next lemma: lemma l1_cl (A B C : Prop) : ((A → B) → C) → ((A ∧ ¬ B) ∨ C) := ...
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251 views

### Problem proving a binary add function

I'm fairly new to the Coq language and I want to prove a function that does an binary add from numbers represented as a list (least significant bit upfront). I have created this badd function that ... 183 views

### Proof of symmetry of universe-polymorphic Leibniz equality in Agda

Consider the following definition of universe-polymorphic Leibniz equality: ...
• 4,740
102 views

### Code Review: Proving that a simple propositional logic satisfies Aristotle's Thesis

I'm proving that a simple propositional logic satisfies Aristotle's thesis. I'm curious how to improve the code in question. Here are the things I know that are wrong with it: I'm using ...
• 2,593
118 views

### How to implement first-order relational structures in Coq?

I'm trying to define a first-order relational structure in Coq. I have a way to define a pre-first-order-relational-structure, which is not a standard notion, but seems simple enough. I also have a ...
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76 views

### Proof Review: Basic theorem about ternary relations in Coq

I'm proving a simple fact about ternary relations in Coq as an exercise. I'm interested in ternary relations at the moment because they are a simple thing that can represent a finitary consequence ...
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Theorem to prove: The sum of the binomial coefficients over an antidiagonal is a Fibonacci number. More specifically, the $n$th antidiagonal sums to the $n+1$th Fibonacci number, where the ...