proposition: Lemma nil_matrix_invertible {n : nat} (A : Matrix R 0 0): matrix_inverse A.
proof: Proof. exists identity_matrix. use tpair. - etrans. apply matrunax2. apply funextfun; intro i. now apply(@iscontr_nil_row_matrix _ 0). - etrans. apply matlunax2. apply funextfun; intro. now apply (@iscontr_nil_row_matrix _ 0). 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