reserve i,j,k,n,m,l,s,t for Nat;
reserve a,b for Real;
reserve F for real-valued FinSequence;
reserve z for Complex;
reserve x,y for Complex;
reserve r,s,t for natural Number;

theorem
  (x*y) |^ s = x|^s * y|^s
proof
  reconsider x, y as Element of COMPLEX by XCMPLX_0:def 2;
  x|^s*y|^s = Product(s |-> (x*y)) by RVSUM_1:113;
  hence thesis;
end;
