proposition: Lemma vecsum_rdistr: ∏ (n : nat) (vec : Vector R n) (s : R), op2 (Σ vec) s = Σ (scalar_rmult_vec vec s).
proof: Proof. intros. induction n as [| n IH]. - apply rigmult0x. - rewrite 2 vecsum_step. rewrite rigrdistr. apply maponpaths_2, IH. Defined.
imports: UniMath.Foundations.PartA UniMath.Foundations.NaturalNumbers UniMath.MoreFoundations.PartA UniMath.MoreFoundations.Nat UniMath.MoreFoundations.Tactics UniMath.Combinatorics.StandardFiniteSets UniMath.Combinatorics.Vectors UniMath.Algebra.RigsAndRings UniMath.Algebra.IteratedBinaryOperations UniMath.Algebra.Matrix UniMath.Algebra.GaussianElimination.Auxiliary