(R : Ring) (m n: nat) : LeftIdentity (@matrix_mult R m m n) (identity_matrix R m). Proof. intros M; apply path_matrix; intros i j Hi Hj. rewrite entry_Build_Matrix. lhs nrapply path_ab_sum. 1: intros k Hk; by rewrite entry_Build_Matrix. nrapply rng_sum_kronecker_delta_l. 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.