reserve i,j,k,n,m for Nat,
  x,y,z,y1,y2 for object, X,Y,D for set,
  p,q for XFinSequence;
reserve k1,k2 for Nat;
reserve D for non empty set,
  F,G for XFinSequence of D,
  b for BinOp of D,
  d,d1,d2 for Element of D;
reserve F for XFinSequence,
        rF,rF1,rF2 for real-valued XFinSequence,
        r for Real,
        cF,cF1,cF2 for complex-valued XFinSequence,
        c,c1,c2 for Complex;

theorem Th54: :: RLVECT_1:58 NUMERAL1:1
  Sum(cF1^cF2)=Sum(cF1)+Sum(cF2)
proof
  thus Sum(cF1^cF2)=addcomplex.(Sum(cF1),Sum(cF2)) by Th41
    .= Sum(cF1)+Sum(cF2) by BINOP_2:def 3;
end;
