let V be strict Z_Module; :: thesis: for A, B being Subset of V st Lin A = V & A c= B holds
Lin B = V
let A, B be Subset of V; :: thesis: ( Lin A = V & A c= B implies Lin B = V )
assume ( Lin A = V & A c= B ) ; :: thesis: Lin B = V
then V is Submodule of Lin B by Th70;
hence Lin B = V by ZMODUL01:41; :: thesis: verum