matrix_transpose_identity@{i} {R : Ring@{i}} {n} : matrix_transpose (identity_matrix R n) = identity_matrix R n. Proof. apply path_matrix. intros i j Hi Hj. rewrite 3 entry_Build_Matrix. apply kronecker_delta_symm. 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.