:: deftheorem Def1 defines Subspace RUSUB_1:def 1 :
for V, b₂ being RealUnitarySpace holds
( b₂ is Subspace of V iff ( the carrier of b₂ c= the carrier of V & 0. b₂ = 0. V & the addF of b₂ = the addF of V || the carrier of b₂ & the Mult of b₂ = the Mult of V | [:REAL, the carrier of b₂:] & the scalar of b₂ = the scalar of V || the carrier of b₂ ) );