theorem Th12: :: LOPBAN15:10

for X being RealLinearSpace-Sequence
for r being Element of REAL
for v being Element of product (carr X)
for i being Element of dom (carr X) holds
( ([:(multop X):] . (r,v)) . i = the Mult of (X . i) . (r,(v . i)) & ( for vi being VECTOR of (X . i) st vi = v . i holds
([:(multop X):] . (r,v)) . i = r * vi ) )