Questions tagged [beginner]

Questions asked by a beginner user of proof assistants. We make an effort to be extra kind to such users.

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Looking for an entry point in the universe of proof assistants and proof IDE's

This is my first question in this part of StackExchange. What I would like to achieve is the following. Suppose I want to study ( or give a course on ) basic Real Analysis, I want to 1) document the ...
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4 votes
0 answers
67 views

Display style proofs using Coq

How to display proofs using in Gentzen tree style and (or) Fitch-style, using CoqIDE or JsCoq? PS: I'm rookie used coq.
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6 votes
1 answer
184 views

How to replace a function by its body

I have this function: Definition bexp x y := bexp_r x y [true]. And I have this goal: value (bexp [] y) = 0 ^ value y I want ...
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2 votes
1 answer
166 views

Lemma about splitting of homogeneous polynomial equations into irreducible equations

Proof assistants, and Lean, are completely new to me. How can I derive the following simple lemma in Lean? How can I let Lean check if the lemma is correctly written? How can I let Lean check if the ...
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  • 131
6 votes
2 answers
245 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 ...
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8 votes
2 answers
650 views

Explanation of Coq math-comp repositories

How are the Coq math-comp account and repositories related? Details One of my side goals is to try to keep the tags on this site meaningful and useful. Today I ran into this question: How to prove ...
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9 votes
1 answer
488 views

How to define curry in Lean

I just started with Lean and with this nice SE. In the official web book/tutorial, when explaining definitions https://leanprover.github.io/theorem_proving_in_lean/index.html they ask to complete this ...
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  • 193
16 votes
1 answer
300 views

Formalizations of unsolved problems

Is there a library (for any proof assistant) which provides formalized definitions of unsolved problems? To clarify, I mean some collection that correctly defines unsolved problems in the language of ...
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  • 489
9 votes
1 answer
155 views

Generating valid statements without a proof goal

Given some initial list of assumptions, I'd like to generate some true statements which follow from them without seeking a specific proof goal. I only need a small number of consequences from those ...
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  • 489
8 votes
2 answers
261 views

Strong induction on ℕ with function α → ℕ

I have the following problem. I have a type $\alpha$, function $f : \alpha \to \mathbb{N}$ and predicate $P : \alpha \to \mathrm{Prop}$ and I want to prove that for all $a : \alpha, P a$. How could ...
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  • 127
3 votes
1 answer
133 views

Coq defining a hierarchy of collections of integers with infinitely many "levels"

I'm trying to formalize a small part of higher-order arithmetic in Coq as an exercise (Wikipedia article for second-order arithmetic). It's straightforward to formalize something resembling second-...
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  • 2,467
9 votes
2 answers
187 views

Comparison between proof assistants for coinductive structures and proofs

I have a quite vague and naïve question: what are the differences between the different proof assistants regarding coinduction? My motivation is that I'd like to formalize some proofs, basically about ...
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2 votes
2 answers
63 views

Coq produce instance of a type `{x : T | P x}` inside an explicit definition given an `x'` of type `T`

I'm trying to formalize a simple type system in Coq as an exercise. I have a type Item and a type {x : Item | IsNormal Item}. If ...
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2 votes
1 answer
94 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 ...
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  • 2,467
13 votes
2 answers
173 views

Tools for checking the consistency of a type theory

My question is twofold: How do you define consistency (analogously to the concept in first-order logic) in the context of a type theory? Are there any tools that can check consistency? I have seen a ...
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  • 2,467
4 votes
1 answer
105 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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  • 2,467
4 votes
1 answer
66 views

Referencing previous fields when constructing new structure

Let's say I have a simple structure structure foo : Type := (a : ℕ) (b : list (fin a)) when defining the field b I can ...
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  • 127
4 votes
2 answers
71 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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  • 2,467
2 votes
1 answer
123 views

Defining Lists and Prove Associativity of Append [closed]

When I saw this question asking what is the "Hello, World!" for proof assistants I immediately thought of that exercise. Not a long time after this answer by Couchy was proposed. Therefore, ...
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13 votes
4 answers
159 views

What mathematical topics should I learn first before I start using proof assistants?

I'm a theoretical computer scientist and my research is focused mainly on structural and algorithmic graph theory. Recently I've been very interested in using proof assistants. As a "pet project&...
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3 votes
3 answers
78 views

How do you import part of the standard library in Coq?

How do you import part of the standard library in Coq? How do you import Nat specifically? Why is reporting Nat not required to ...
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  • 2,467
9 votes
1 answer
102 views

Representing $\Bbb RP^2$ in Lean: building a type representing a particular set

I need to work with the set of all lines in the Cartesian plane. For my context, the natural way to think of this is that a line can be described by an equation $Ax + By + C = 0$, where $A$ and $B$ ...
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  • 285
14 votes
2 answers
172 views

What is the difference between refl and rfl in Lean 3?

I already know that refl is called a tactic, and that rfl is a term; can you explain with examples how they technically differ? ...
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31 votes
8 answers
906 views

Proof assistants for beginners - a comparison

What is a good starting point to learn about proof assistants? The answer will invariably depend on the area of interest: mathematics (and its areas, e.g. algebra,combinatorics, analysis, logic), CS - ...
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