{R : Ring} {m n} (r : R) (M : Matrix R m n) : matrix_transpose (matrix_lact r M) = matrix_lact r (matrix_transpose M). Proof. apply path_matrix. intros i j Hi Hj. by rewrite !entry_Build_Matrix, !entry_Build_Vector. 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.