:: deftheorem Def2 defines Subspace RLSUB_1:def 2 :
for V, b₂ being RealLinearSpace 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:] ) );