let V be strict RealLinearSpace; :: thesis: for A being Subset of st A = the carrier of V holds
Lin A = V
let A be Subset of ; :: thesis: ( A = the carrier of V implies Lin A = V )
assume A = the carrier of V ; :: thesis: Lin A = V
then A = the carrier of ((Omega). V) ;
hence Lin A = V by Th21; :: thesis: verum