let p be Real; :: thesis: ( 1 <= p implies RLSStruct(# (the_set_of_RealSequences_l^ p),(Zero_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)),(Add_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)),(Mult_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)) #) is Subspace of Linear_Space_of_RealSequences )
assume 1 <= p ; :: thesis: RLSStruct(# (the_set_of_RealSequences_l^ p),(Zero_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)),(Add_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)),(Mult_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)) #) is Subspace of Linear_Space_of_RealSequences
then the_set_of_RealSequences_l^ p is linearly-closed by Th4;
hence RLSStruct(# (the_set_of_RealSequences_l^ p),(Zero_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)),(Add_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)),(Mult_ ((the_set_of_RealSequences_l^ p),Linear_Space_of_RealSequences)) #) is Subspace of Linear_Space_of_RealSequences by RSSPACE:11; :: thesis: verum