proposition: Lemma ex5m_prop2: has_infimum (Vg Er k) (ex5_mij_J J k x).
proof: Proof. move:(proj1 mp2)(mp1) => jI [_ nej fsj]. have fs: finite_set (ex5_mij_J J k x) by apply: finite_fun_image. have ne:nonempty (ex5_mij_J J k x) by apply:funI_setne. exact: (lattice_finite_inf2 (lEr jI) fs ne ex5m_prop1). Qed.
imports: mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat)