reserve s for set,
  i,j for Nat,
  c,c1,c2,c3 for Complex,
  F,F1,F2 for complex-valued FinSequence,
  R,R1,R2 for i-element complex-valued FinSequence;

theorem
  (i|->c1) + (i|->c2) = i|->(c1+c2)
proof
  reconsider s1=c1, s2=c2 as Element of COMPLEX by XCMPLX_0:def 2;
  (i|->s1) + (i|->s2) = i|->(addcomplex.(s1,s2)) by FINSEQOP:17
    .= i|->(c1+c2) by BINOP_2:def 3;
  hence thesis;
end;
