I have a term rewriting system (A, →) where A is a set and → a infix binary relation on A. Given x and y of A, x → y means that x reduces to y.
To implement some properties I simply use the definitions from Coq.Relations.Relation_Definitions and Coq.Relations.Relation_Operators.
Now I want to formalize the following property :
- → is terminating, that is : there is no infinite descending chain a0 → a1 → ...
How can I achieve that in Coq ?