(R : Type) (m n : nat) (M_fun : forall (i : nat) (j : nat), (i < m)%nat -> (j < n)%nat -> R) : Matrix R m n. Proof. snrapply Build_Vector. intros i Hi. snrapply Build_Vector. intros j Hj. exact (M_fun i j Hi Hj). Defined.
Require Import Basics.Overture Basics.Trunc Basics.Tactics Basics.Decidable. Require Import Types.Sigma. Require Import Spaces.List.Core Spaces.List.Theory Spaces.List.Paths. Require Import Algebra.Rings.Ring Algebra.Rings.Module Algebra.Rings.CRing Require Import abstract_algebra. Require Import WildCat.Core WildCat.Paths. Require Import Modalities.ReflectiveSubuniverse.