let i be Nat; :: thesis: for R1, R2 being i -element complex-valued FinSequence holds Sum (R1 + R2) = (Sum R1) + (Sum R2)
let R1, R2 be i -element complex-valued FinSequence; :: thesis: Sum (R1 + R2) = (Sum R1) + (Sum R2)
reconsider R1 = R1, R2 = R2 as i -element FinSequence of COMPLEX by FINSEQ_1:102;
reconsider T1 = R1, T2 = R2 as Element of i -tuples_on COMPLEX by FINSEQ_2:131;
Sum (R1 + R2) = addcomplex . ((addcomplex $$ T1),(addcomplex $$ T2)) by SETWOP_2:35
.= (Sum R1) + (Sum R2) by BINOP_2:def 3 ;
hence Sum (R1 + R2) = (Sum R1) + (Sum R2) ; :: thesis: verum