Research proof index

Universal property (extension) for the Dedekind–MacNeille completion. Given an order embedding f : α ↪o β into a complete lattice β, this theorem produces an order embedding f' : DedekindMacNeilleCompletion α ↪o β such that f = f' ∘ coe'. API note: the constructed f' is defined by a sSup over lower bounds of upper bounds of the image of x. T...