let R be Skew-Field; :: thesis: for V being LeftMod of
for A being Subset of st Lin A = V holds
ex I being Basis of V st I c= A
let V be LeftMod of ; :: thesis: for A being Subset of st Lin A = V holds
ex I being Basis of V st I c= A
let A be Subset of ; :: thesis: ( Lin A = V implies ex I being Basis of V st I c= A )
assume Lin A = V ; :: thesis: ex I being Basis of V st I c= A
then consider B being Subset of such that
A1: B c= A and
A2: B is base by Th27;
reconsider B = B as Basis of V by A2, Def5;
take B ; :: thesis: B c= A
thus B c= A by A1; :: thesis: verum