let c1, c2, c3, c4, c5, c6, c7, c8 be Complex; :: thesis: Sum <*c1,c2,c3,c4,c5,c6,c7,c8*> = ((((((c1 + c2) + c3) + c4) + c5) + c6) + c7) + c8
Sum <*c1,c2,c3,c4,c5*> = (((c1 + c2) + c3) + c4) + c5 by Th21;
then ((((c1 + c2) + c3) + c4) + c5) + ((c6 + c7) + c8) = (Sum <*c1,c2,c3,c4,c5*>) + (Sum <*c6,c7,c8*>) by RVSUM_2:35
.= Sum <*c1,c2,c3,c4,c5,c6,c7,c8*> by RVSUM_2:32 ;
hence Sum <*c1,c2,c3,c4,c5,c6,c7,c8*> = ((((((c1 + c2) + c3) + c4) + c5) + c6) + c7) + c8 ; :: thesis: verum