I am writing Coq code that needs to modify lists, particularly by accessing an index i, applying a function to that element, and replacing it back. I ...

I have a tactic whose expected behavior is to output an error message, and I want to run it in batch mode on a series of goals and for each goal, I wa ...

I have a problem in proving trivial proposition. First, We define a composition of function with general domain and codomain: We will now try to p ...

In many parts of the standard library, there are a bunch of OCaml-native functions with no Coq counterpart. I implemented a Coq version of some of the ...

I have trees of arbitrary arity, with the following type: I can easily create a number of Fixpoint functions such as the following one: but none ...

I want to rewrite a term, as a function in a sort of beta expansion (inverse of beta reduction). So, for example in the term a + 1 = RHS I would like ...

Check nat. (* => Set *) But I'm able to pass nat to functions that take a parameter of type Type, even though Set and Type aren't the same. That b ...

I'm really annoyed by the following goal: where a is a nat. The only lemma that seems to help is unitrE, but then it seems impossible to simplify f ...

I am trying to apply the addf_div theorem from math-comp's ssralg to the following: 1 / a%:R + 1 / a%:R. I want to show that this is 2 / a%:R, but ad ...

I have the following project structure: 'defn.v' has some definitions and compiles perfectly with coqc command. However, I want to import definitio ...

In Software Foundations, they discuss how to build you own proof objects for induction: https://softwarefoundations.cis.upenn.edu/lf-current/IndPrinci ...

Is there a way to destruct and rewrite simultaneously? Here's a toy example. Basically, this is easily provable by destructing q x, but attempting ...

I'm experimenting with lists in Coq: The Arguments statements at the bottom (in addition to some Notation statements) allow me to write [1;2;3] and ...

I'm attempting to use Fix to express a well-founded function. It has Fix_eq to unwrap it for 1 level, however, the confusing part is that Fix_eq is ex ...

Is it possible to rewrite something that uses variables from another scope, such as a function call that uses a variable from a match, fun, or fix ? F ...

The definition of int comes from compcert, I wanna prove foo, suppose that the induction strategy needs to be used, because there is a recursive re ...

I don't know how can I prove this theorem, since I can not link oddn with evenn. For the second problem, I got stuck because the recursion I defi ...

Error: Cannot guess decreasing argument of fix. I Defined a function according to the description above, but it seems that Coq cannot deal with thi ...

I'm trying to prove equivalency for a pretty common "bitwise hack", namely: 0 < m /\ land m (m - 1) = 0 -> modulo i m = land i (m - 1): modu ...

I'm trying to understand the iris, a state-of-art verification framework based on separation logic. lang.v is the default language used by Iris. Follo ...