We introduce a notion of strong proximity join-semilattice. a predicative notion of continuous lattice which arises as the Karoubi envelop of the category of algebraic lattices. Strong proximity join-semilattices can be characterised by the coalgebras of the lower powerlocale on the wider category of proximity posets (also known as abstract bases or R-structures). Moreover. https://thebrickes.shop/product-category/queen-mattress-set/