:: deftheorem Def1 defines the_set_of_BoundedRealSequences RSSPACE4:def 1 :
for b₁ being Subset of Linear_Space_of_RealSequences holds
( b₁ = the_set_of_BoundedRealSequences iff for x being object holds
( x in b₁ iff ( x in the_set_of_RealSequences & seq_id x is bounded ) ) );