fact: Definition lower_semicontinuous f := forall x a, a%:E < f x -> exists2 V, nbhs x V & forall y, V y -> a%:E < f y.
imports: HB(structures) mathcomp(all_ssreflect ssralg ssrint ssrnum finmap matrix) mathcomp(rat interval zmodp vector fieldext falgebra) mathcomp(mathcomp_extra boolp classical_sets functions) mathcomp(cardinality set_interval Rstruct) ereal reals signed topology prodnormedzmodule