Questions tagged [beginner]
Questions asked by a beginner user of proof assistants. We make an effort to be extra kind to such users.
90
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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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20
votes
2
answers
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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? ...
- 410
16
votes
1
answer
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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 ...
- 519
14
votes
2
answers
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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 ...
- 3,095
14
votes
4
answers
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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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13
votes
1
answer
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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 $B$ ...
- 367
9
votes
2
answers
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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 ...
- 229
9
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1
answer
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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 ...
- 193
9
votes
1
answer
181
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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 ...
- 519
8
votes
2
answers
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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 ...
- 2,846
8
votes
2
answers
533
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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 ...
- 137
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3
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Why is $\Bbb Z = \Bbb N$ independent of Lean?
In this answer, it is noted
For a silly example, in ZFC with the usual encoding, $\mathbb{Z} \neq \mathbb{N}$, but in Lean it is well-known that this is independent. Of course in both ZFC or Lean, ...
- 173
7
votes
1
answer
924
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What is the current state of proof assistants?
I am a high school senior going into college and I am applying to a scholarship in which I must write an essay about a potential future technology that would dramatically impact humans. I immediately ...
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6
votes
1
answer
334
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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 ...
user1231
6
votes
2
answers
274
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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 ...
user1231
6
votes
1
answer
243
views
What are some good resources for Proof Assistant based exercises/puzzles for recreation and practice?
Proof Assistant based exercises and puzzles make for a good recreational activity, as well as help sharpen skills of users of said systems. There are many such equivalent resources for algorithmic ...
- 1,502
5
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4
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Less ridiculous way to prove that an Ascii character compares equal with itself in Coq
How do you prove that an Ascii character compares equal with itself in Coq idiomatically?
In the course of trying to prove a random exercise in Logical Foundations, I wanted to prove the following ...
- 3,095
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votes
3
answers
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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 ...
- 3,095
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votes
2
answers
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How do I express a negative premise in Coq?
I would like to express a transition system in the style of the small-step operational semantics as found in volume 2 of "Software foundations". Unfortunately my transition system has rules ...
- 282
5
votes
2
answers
290
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Unclarity about Preorder class in Lean4
I realize the port of Mathlib to Lean4 is not finished yet, but I've run into a definition that I do not quite understand. I'm quite new at using theoremprovers as well as stackexchange, so please be ...
- 153
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1
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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 ...
- 3,095
5
votes
1
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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 ...
- 137
5
votes
1
answer
524
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Why is lean 4 behaving differently on my machine vs in the natural number game?
In the lean 4 version of the natural number game at https://adam.math.hhu.de/#/g/leanprover-community/NNG4/ , I can use tactics like apply x at h and ...
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1
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How to prove a property of a conditional statement without using tactics in Lean?
This doesn't work even though it is the simplest proof of an if statement that I can think of:
...
5
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1
answer
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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 ...
- 151
5
votes
1
answer
702
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How to unfold definitions in Lean / find the right theorems to apply?
After a few days playing around with Lean4, I notice I keep running into the problem of how to find the right theorems to apply. The situation below is one I run into particularly often, so perhaps I ...
- 153
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votes
1
answer
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Is there an easy-to-learn GUI of proof assistants for teenagers in maths education?
I'm a high school sophomore and I have been interested in Interactive Theorem Proving for a year or two. I found it extremely hard for my peers (lack of knowledge in mathematical logic, type theories ...
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votes
0
answers
109
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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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votes
2
answers
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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 ...
- 3,095
4
votes
2
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210
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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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