Definition back_sub_stmt { n : nat } {F : fld} (mat : Matrix F n n) (vec : Vector F n) (ut : @is_upper_triangular F _ _ mat) (df : @diagonal_all_nonzero F _ mat) := ∑ v : (Vector F n), (@matrix_mult F _ _ mat _ (col_vec v)) = (col_vec vec).
Require Import UniMath.MoreFoundations.PartA. Require Import UniMath.MoreFoundations.Nat. Require Import UniMath.MoreFoundations.Tactics. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.Domains_and_Fields. Require Import UniMath.Algebra.Matrix. Require Import UniMath.Algebra.RigsAndRings. Require Import UniMath.Algebra.IteratedBinaryOperations. Require Import UniMath.Algebra.GaussianElimination.Auxiliary. Require Import UniMath.Algebra.GaussianElimination.Vectors. Require Import UniMath.Algebra.GaussianElimination.Matrices. Require Import UniMath.Algebra.GaussianElimination.Elimination.