A1: p (/) r is FinSequence of REAL by RVSUM_1:145;
A2: len p = n by CARD_1:def 7;
Seg (len (p (/) r)) = dom (p (/) r) by FINSEQ_1:def 3
.= dom p by VALUED_1:def 5
.= Seg n by A2, FINSEQ_1:def 3 ;
then len (p (/) r) = n by FINSEQ_1:6;
hence p (/) r is Element of REAL n by A1, FINSEQ_2:92; :: thesis: verum