{R : Ring} (I J : Subgroup R) : R -> Type := | ipn_in : forall x y, I x -> J y -> I J (x * y).
Require Import Basics Types. Require Import Spaces.Finite.Fin. Require Import Classes.interfaces.canonical_names. Require Import Algebra.Rings.Ring. Require Import Algebra.Groups.Subgroup. Require Import Algebra.AbGroups. Require Import WildCat.Core. Module Import Notation.