proposition: Lemma matrix_left_inverse_to_transpose_right_inverse {m n} (A : Matrix CR m n) (inv: @matrix_left_inverse CR m n A) : (@matrix_right_inverse CR n m (@transpose CR n m A)).
proof: Proof. destruct inv as [inv isinv]. exists (transpose inv). etrans. { apply pathsinv0, matrix_product_transpose. } etrans. { apply maponpaths, isinv. } apply identity_matrix_symmetric. 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