proposition: Lemma vector_1_inj { X : rig } { n : nat } (e1 e2 : X) : (λ y : (⟦ 1 ⟧)%stn, e1) = (λ y : (⟦ 1 ⟧)%stn, e2) -> e1 = e2.
proof: Proof. intros eq; apply (invmaponpathsweq (@weq_vector_1 X) _ _ eq). 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