fact: Definition prl_ne1_condii' i:= forall F, sub F (Vg FS_fam i) -> nonempty F -> ~(inc emptyset F) -> (forall x y, inc x F -> inc y F -> exists z, [/\ inc z F, sub z x & sub z y]) -> nonempty (intersection F).
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)