reserve s for set,
  i,j for natural Number,
  k for Nat,
  x,x1,x2,x3 for Real,
  r,r1,r2,r3,r4 for Real,
  F,F1,F2,F3 for real-valued FinSequence,
  R,R1,R2 for Element of i-tuples_on REAL;

theorem Th89:
  Sum(R1 + R2) = Sum R1 + Sum R2
proof
  i is Nat by TARSKI:1;
  hence Sum(R1 + R2) = addreal.(addreal$$R1,addreal$$R2) by SETWOP_2:35
    .= Sum R1 + Sum R2 by BINOP_2:def 9;
end;
