let R be domRing; :: thesis: for V being strict LeftMod of strict
for A, B being Subset of st Lin A = V & A c= B holds
Lin B = V
let V be strict LeftMod of strict ; :: thesis: for A, B being Subset of st Lin A = V & A c= B holds
Lin B = V
let A, B be Subset of ; :: 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 Subspace of Lin B by Th15;
hence Lin B = V by VECTSP_4:33; :: thesis: verum