let i be Nat; :: thesis: for R1, R2 being i -long FinSequence of COMPLEX holds Sum (R1 + R2) = (Sum R1) + (Sum R2)
let R1, R2 be i -long FinSequence of COMPLEX ; :: thesis: Sum (R1 + R2) = (Sum R1) + (Sum R2)
reconsider T1 = R1, T2 = R2 as Element of i -tuples_on COMPLEX by FINSEQ_2:151;
thus Sum (R1 + R2) = addcomplex . (addcomplex $$ T1),(addcomplex $$ T2) by SETWOP_2:46
.= (Sum R1) + (Sum R2) by BINOP_2:def 3 ; :: thesis: verum