# Questions tagged [definition]

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### Packaging Mathematical Structures in Coq: Help Understanding a Definition

Context I am a relatively new user to Coq with a decent understanding of the basics of dependent type theory and am midway through chapter 2 of the Software Foundations Series of books. I want to ...
134 views

### Is there a way to rename parameters when including/reusing a module type in Coq?

Say I have a (more general) module type Collection that specifies some operations like read and write and now I want to create (more specialized) module types like <...
1 vote
91 views

### Defining a Recursive Function decreasing on one argument with < and another structurally

I want to define a function which decreases in one argument using < and on another structurally. What is the least painful way to do this? Among the many options (Function, Program Fixpoint, ...
76 views

### How do clausal definitions work?

I'm most familiar with the metatheory of calculi based around expressions. But systems like Agda use separate clauses for definitions. ...
252 views

### 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 ...
1 vote
61 views

### Question about default definitions in fields

In Unclarity about Preorder class in Lean4 I asked why the third and fourth field (lt and lt_iff_le_not_le) in the definition of MyPreorder below would both be necessary, as one follows from the other ...
80 views

### Define a function using another function

I want to define a translation function g from another function f. Definition trans (f g : Q -> Q) (t : Q) := forall q : Q, f (q + t) == g q. In the above code,...
217 views

### An algorithm for the substitution of formulas for predicates in first order logic

I am trying to find a detailed description of the definition of substitution of formulas for predicates in first order logic and an implementation of this as a function in Lean or Haskell. The aim is ...
203 views

### 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-...