Definition add_row_mult_target_row {m n} (r1 r2 : ⟦ m ⟧%stn) (s : R) (mat : Matrix R m n) (c : ⟦ n ⟧%stn) : (add_row_mult r1 r2 s mat) r2 c = (mat r2 c + s * mat r1 c)%rig. Proof. unfold add_row_mult. now rewrite stn_eq_or_neq_refl. 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.