On Well Founded sets and the Axiom of Choice

Prove that, if we admit the axiom of functional choice (look at library Logic.ClassicalChoice), then if some relation R is not well founded, there exists a strictly decreasing (w.r.t. R) infinite sequence.

Remarks

Look also at that exercise
The Axiom of Functional Choice is presented on Coq's FAQ (in Coq's documentation ). Look at the section "The Logic of Coq : Axioms".

Solution

Look at this file .