proposition: Lemma zero_row_to_non_invertibility { n : nat } (A : Matrix R n n) (i : ⟦ n ⟧%stn) (zero_row : A i = (const_vec 0%ring)) : (@matrix_inverse R n A) -> empty.
proof: Proof. intros invA. apply matrix_inverse_to_right_and_left_inverse in invA. destruct invA as [? rinvA]. apply (zero_row_to_non_right_invertibility A i); 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