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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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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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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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
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2
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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 ...
- 3,073
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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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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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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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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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1
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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
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2
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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
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votes
2
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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 ...
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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
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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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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
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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