Definition is_upper_triangular_partial { m n k : nat } (mat : Matrix R m n) := ∏ (i : ⟦ m ⟧%stn ) (j : ⟦ n ⟧%stn ), (stntonat _ i > (stntonat _ j)) -> i < k -> (mat i j) = 0%rig.
Require Import UniMath.Foundations.All. Require Import UniMath.MoreFoundations.All. Require Import UniMath.Combinatorics.StandardFiniteSets. Require Import UniMath.Combinatorics.Vectors. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors.