proposition: Lemma invertible_to_transpose_invertible { n } (mat : Matrix CR n n) : (@matrix_inverse CR n mat) -> (@matrix_inverse CR n (transpose mat)).
proof: Proof. intros [mat_inv [e_mi e_im]]. exists (transpose mat_inv). split; refine (!matrix_product_transpose _ _ @ maponpaths _ _ @ identity_matrix_symmetric); assumption. 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