proposition: Lemma matrix_mult_zero_vec_eq {m n : nat} {mat : Matrix R m n} : mat ** col_vec (const_vec 0%rig) = col_vec (const_vec 0%rig).
proof: Proof. rewrite matrix_mult_eq; unfold matrix_mult_unf. apply funextfun; intros i. unfold col_vec. apply funextfun; intros _. apply vecsum_eq_zero. intros k. apply rigmultx0. Defined.
imports: UniMath.Foundations.All UniMath.MoreFoundations.All UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.Algebra.RigsAndRings UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.Matrix UniMath.Algebra.Domains_and_Fields UniMath.Algebra.GaussianElimination.Auxiliary UniMath.Algebra.GaussianElimination.Vectors