let V be finite-dimensional RealUnitarySpace; :: thesis: dim V = dim ((Omega). V)
consider I being finite Subset of V such that
A1: I is Basis of V by Def1;
A2: (Omega). V = UNITSTR(# the carrier of V, the ZeroF of V, the addF of V, the Mult of V, the scalar of V #) by RUSUB_1:def 3
.= Lin I by A1, RUSUB_3:def 2 ;
( card I = dim V & I is linearly-independent ) by A1, Def2, RUSUB_3:def 2;
hence dim V = dim ((Omega). V) by A2, Th9; :: thesis: verum