Injectivity of the surviving-branch map

theorem MagnitudeConjecture.BoundQuiver.StringPresentation.otherIncomingFamilyToCokernelRadical_injective {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) : Function.Injective ⇑(P.otherIncomingFamilyToCokernelRadical a)