let V be ComplexLinearSpace; :: thesis: for W being Subspace of V
for x being set st x in W holds
x in V
let W be Subspace of V; :: thesis: for x being set st x in W holds
x in V
let x be set ; :: thesis: ( x in W implies x in V )
assume x in W ; :: thesis: x in V
then ( x in the carrier of W & the carrier of W c= the carrier of V ) by Def5, STRUCT_0:def 5;
hence x in V by STRUCT_0:def 5; :: thesis: verum