reserve x,y for object,
        D,D1,D2 for non empty set,
        i,j,k,m,n for Nat,
        f,g for FinSequence of D*,
        f1 for FinSequence of D1*,
        f2 for FinSequence of D2*;
reserve f for complex-valued Function,
        g,h for complex-valued FinSequence;

theorem Th17:
  (h,0) +...+ (h,k) = (h,1) +...+ (h,k)
proof
  not 0 in dom h by FINSEQ_3:25;
  then A1:h.0 = 0 by FUNCT_1:def 2;
  (h,0) +...+ (h,k) = h.0+(h,0+1) +...+ (h,k) by Th13;
  hence thesis by A1;
end;
