let GF be Field; :: thesis: for V being strict VectSp of strict
for A, B being Subset of st Lin A = V & A c= B holds
Lin B = V
let V be strict VectSp 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 Th18;
hence Lin B = V by VECTSP_4:33; :: thesis: verum