Definition add_row_mult { m n } (r1 r2 : ⟦ m ⟧%stn) (s : R) (mat : Matrix R m n) : ( Matrix R m n ). Proof. intros i j. induction (stn_eq_or_neq i r2). - exact ((mat r2 j) + (s * (mat r1 j)))%rig. - exact (mat i j). Defined.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.Vectors. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors. Require Import UniMath.Algebra.GaussianElimination.Matrices.