{R : CRing} {m n p} (M : Matrix R m n) (N : Matrix R n p) : matrix_transpose (matrix_mult M N) = matrix_mult (matrix_transpose N) (matrix_transpose M). Proof. lhs nrapply matrix_transpose_mult. apply matrix_mult_rng_op. 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.