
theorem Th25:
  for a, b being Ordinal holds Sum^ <% a, b %> = a +^ b
proof
  let a, b be Ordinal;
  thus Sum^ <% a, b %> = Sum^ (<%a%>^<%b%>) by AFINSQ_1:def 5
    .= Sum^ <%a%> +^ Sum^ <%b%> by Th24
    .= Sum^ <%a%> +^ b by ORDINAL5:53
    .= a +^ b by ORDINAL5:53;
end;
