proposition: Lemma back_sub_internal_inv1 { n : nat } (mat : Matrix F n n) (x : Vector F n) (b : Vector F n) (ut : @is_upper_triangular F _ _ mat) (sep : ⟦ S n ⟧%stn) (row : ⟦ S n ⟧%stn) : ∏ i : stn n, i >= row -> (back_sub_internal mat x b sep row) i = x i.
proof: Proof. intros. rewrite (@col_vec_inj_pointwise F n (back_sub_internal mat x b sep row) x i). - apply idpath. - now apply (back_sub_internal_inv0). Defined.
imports: UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Nat UniMath.MoreFoundations.Tactics UniMath.Algebra.Matrix UniMath.Algebra.Domains_and_Fields UniMath.Algebra.Matrix UniMath.Algebra.RigsAndRings UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.GaussianElimination.Auxiliary UniMath.Algebra.GaussianElimination.Vectors UniMath.Algebra.GaussianElimination.Matrices UniMath.Algebra.GaussianElimination.Elimination