{R : CRing} {m n p} (M : Matrix R m n) (N : Matrix R n p) : matrix_mult (R:=rng_op R) M N = matrix_mult M N. Proof. apply path_matrix; intros i j Hi Hj. rewrite 2 entry_Build_Matrix. apply path_ab_sum; intros k Hk. apply rng_mult_comm. 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.