All Questions
1,062
questions
0
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1
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19
views
Prove that a function's result cannot dependent on Prop-valued parameters in Coq
Consider the following function elem and the lemma that the result of elem does not depend on the proof of ...
- 155
2
votes
3
answers
160
views
Uniqueness of proofs for inductively defined predicates
In Init/Peano.v the less-than-or-equal predicate is defined as follows:
...
- 127
0
votes
0
answers
32
views
Found no matching subterm in goal while it does seem to be there when doing rewrite
I have two places in my code which are very similar. I want to apply rewrite there. In the first place it works fine. In the other not. Why not?
First place (works fine):
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2
votes
2
answers
102
views
Type inference with type classes in Coq
I don't understand type classes in Coq. I tried to use them as follows. I have a type cat that is supposed to represent the type of categories and I define the type ...
- 249
0
votes
1
answer
27
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 ...
- 159
1
vote
1
answer
36
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 ...
- 159
1
vote
0
answers
33
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
86
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
76
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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- 159
2
votes
3
answers
546
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 ...
- 3,073
2
votes
2
answers
40
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:
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1
vote
1
answer
71
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:
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- 159
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 ...
- 3,073
2
votes
1
answer
96
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
2
votes
1
answer
64
views
Strategies for representing proofs of equality
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 ...
- 3,073