Module-theoretic indecomposability of represented string-arrow ranges

theorem MagnitudeConjecture.BoundQuiver.StringPresentation.representedArrowLinearRange_isIndecomposableModule {k A Q : Type u} [Field k] [Ring A] [Algebra k A] [Fintype Q] [Quiver Q] [(x y : Q) → Fintype (x ⟶ y)] (P : StringPresentation k A Q) {x y : Q} (a : x ⟶ y) : QuotientSubmoduleEquidistribution.Foundation.IsIndecomposableModule P.quotientCategoryAlgebraᵐᵒᵖ ↥(P.representedArrowLinearMap a).range

A nonzero uniserial represented arrow range is indecomposable as a module.