All Questions
1,058
questions
0
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1
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6
views
What to import to use le_not_gt_iff?
According to the documentation, there should be a Lemma le_not_gt_iff in Coq.Structures.OrdersFacts, but I haven't succeeded in referencing it.
I am trying to prove ...
- 149
0
votes
1
answer
27
views
Arguing with sumbools
I have the following definitions:
Variables Sd_pre : nat -> Prop.
Definition Sd_dec : forall t, { Sd_pre t } + { ~Sd_pre t }.
Admitted.
And the following are ...
- 149
1
vote
0
answers
23
views
Using Isabelle's Archive of Formal Proofs
I am new to Isabelle proof assistant and want to use it to verify a standard proof of the Bruck Ryser Chowla theorem. Since this theorem is about symmetric block designs, I figured that the folder ...
- 111
3
votes
2
answers
75
views
A $\mu$-recursive function converges at an input, how to find the output?
Summary: I want to implement an interpreter for $\mu$-recursive functions which, for any $\mu$-recursive function $f$ and input $\mathbf{x}$, returns $f \left( \mathbf{x} \right)$ if it is defined.
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- 83
3
votes
2
answers
75
views
Using if in Fixpoint
I have this recursive function I am trying to define by way of Fixpoint, but the if condition is giving me trouble.
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- 149
2
votes
3
answers
532
views
What is a positive coinductive type and why are they so bad?
What is a positive coinductive type and why are they so bad?
This question is specifically within the context of Coq and is inspired by this question, the opening lines of which are:
Since positive ...
- 3,053
2
votes
2
answers
39
views
Determining the minimal index where lexicographically different lists diverge in Lean 4
I'm trying to define the smallest index at which two lexicographically different lists of equal length diverge. This is what I have so far:
...
1
vote
1
answer
69
views
Best practices: Should I prefer definitions or iff when defining predicates?
I am a beginner in Coq, and I have a proposition I defined in this way:
...
- 149
5
votes
4
answers
2k
views
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 ...
- 3,053
2
votes
1
answer
93
views
Is there any way to approximate noncomputable functions in Lean4?
As you may know, there are some definitions in lean4 that can't be evaluated due to the noncomputable tag. Is there any way to approximate their value in lean4?
For ...
- 21
0
votes
0
answers
32
views
Strategies for representing proofs of equality [duplicate]
I am interested in strategies for representing proof terms inside the kernel of a proof assistant, specifically proofs of equality.
What are the different strategies that are available for ...
- 3,053
3
votes
1
answer
199
views
Finding reflexive, transitive closure
I got a relation like: R: A -> A -> bool.
Using this, I need to find an Rclose: A -> A -> bool such that ...
- 131
1
vote
1
answer
26
views
Feeding rewrites and other hints into an omnibus tactic
How do I feed rewrites that I've marked as safe into a custom tactic?
I'm trying to write shorter Coq proofs with more of the easy stuff hidden. To that end, in the script below I proved that ...
- 3,053
1
vote
4
answers
199
views
Formalizing "finite or infinite" in Coq
In Coq, I am trying to formalize the notion of a finite or infinite sequence, e.g. of natural numbers: call it a run, and call ...
- 249
4
votes
1
answer
126
views
How to perform type conversion/coercion in Lean 4?
Does Lean 4 have a good way of handling data type conversion (e.g. between the natural and real numbers)?
I am trying to solve the following property from the Mechanics of Proof book:
$\forall a \in Z,...
- 2,210