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 Th11:
  (f,k) +...+ (f,k) = f.k
proof
  consider h be complex-valued FinSequence such that
  A1:(f,k) +...+ (f,k) = Sum h & len h = k-'k+1 &
  (h.(0+1) = f.(0+k) & ... & h.(k-'k+1) = f.(k-'k+k)) by Th9;
  k-'k+1 = 0+1 by XREAL_1:232;
  then h = <*h.1*> by A1,FINSEQ_1:40;
  then Sum h = h.1 by RVSUM_2:30;
  hence thesis by A1;
end;
