Generation of immersed Lagrangians by cocores

We extend the generation theorem of Chantraine–Dimitroglou Rizell–Ghiggini–Golovko to exact Lagrangian immersions in Weinstein manifolds. We prove that an exact Lagrangian immersion equipped with an augmentation of the Chekanov–Eliashberg algebra of its Legendrian lift, or equivalently, equipped with a corresponding bounding cochain, is generated by the Lagrangian cocores.