proposition: Lemma sum_stdb_vector_pointwise_prod { n : nat } (v : Vector R n) (i : ⟦ n ⟧%stn) : Σ (stdb_vector i *pw v) = (v i).
proof: Proof. etrans. { apply (pulse_function_sums_to_point _ i) , (pulse_prod_is_pulse _ _ ) , is_pulse_function_stdb_vector. } unfold pointwise, stdb_vector. rewrite stn_eq_or_neq_refl. apply riglunax2. 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