Show that in the subgroup-intermediate subfield given in the fundamental theorem of Galois Theory, the subfield corresponding to the intersection of two subgroups H1 "and " H2 is the subfield generated by the corresponding intermediate fields ("Inv" H1 "and Inv" H2), and the intersection of two intermediate fields K1 and K2 corresponds to the subgroup generated by the corresponding subgroups "Gal" E/K1 and "Gal" E/K2.