theorem Th1: :: RMOD_4:1

for R being Ring
for V being RightMod of R
for a being Scalar of R
for F, G being FinSequence of V st len F = len G & ( for k being Nat
for v being Vector of V st k in dom F & v = G . k holds
F . k = v * a ) holds
Sum F = (Sum G) * a