proposition: Lemma gaussian_elimination_width_0 {m n} (A : Matrix F m n) {eq0 : 0 = n} : ∑ (B : Matrix F _ _), (@matrix_inverse F _ B) × (is_row_echelon (B ** A)).
proof: Proof. exists (@identity_matrix F m). use tpair. { apply identity_matrix_invertible. } rewrite matlunax2. apply is_row_echelon_nil_matrix; now rewrite eq0. Defined.
imports: UniMath.Foundations.PartA UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Nat UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.FiniteSequences UniMath.Combinatorics.Vectors UniMath.Combinatorics.Maybe UniMath.Algebra.BinaryOperations UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.RigsAndRings UniMath.Algebra.Matrix UniMath.Algebra.Domains_and_Fields UniMath.Algebra.GaussianElimination.Auxiliary UniMath.Algebra.GaussianElimination.Vectors UniMath.Algebra.GaussianElimination.Matrices UniMath.Algebra.GaussianElimination.RowOps