let V be RealUnitarySpace; :: thesis: for I being Basis of V
for v being VECTOR of V holds v in Lin I
let I be Basis of V; :: thesis: for v being VECTOR of V holds v in Lin I
let v be VECTOR of V; :: thesis: v in Lin I
v in UNITSTR(# the carrier of V, the ZeroF of V, the U5 of V, the Mult of V, the scalar of V #) by STRUCT_0:def 5;
hence v in Lin I by Def2; :: thesis: verum