reserve a,b,i,j,k,l,m,n for Nat;

theorem
  for a,b,c be Real holds Sum ((a+b,c) In_Power n) = Sum((a,b+c) In_Power n)
proof
  let a,b,c be Real;
  Sum (((a+b),c) In_Power n) = (a+b+c)|^n by NEWTON:30
  .= (a+(b+c))|^n
  .= Sum ((a,b+c) In_Power n) by NEWTON:30;
  hence thesis;
end;
