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;

then p (#) r is Element of REAL n by A1, FINSEQ_2:92;

hence r (#) p is Point of (TOP-REAL n) by EUCLID:22; :: thesis: verum

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;

then p (#) r is Element of REAL n by A1, FINSEQ_2:92;

hence r (#) p is Point of (TOP-REAL n) by EUCLID:22; :: thesis: verum