Wash Sale Clarification - trading the same security at intervals

Hi All - just a clarification, as the reporting I'm receiving from my broker is confusing (they say they use wash sale logic/rules).   If I have an equity X and I bought 100 shares in say October, then again I bought 100 shares of equity X in early December, but on Dec 30 i sold 100 shares of equity X, that would not be a wash sale, correct? Because I am relieving the first lot of 100 and not the second one (the second one being a sale within 30 days).  I'm trying to determine if the realized loss i took on the 100 share sale on Dec 30 would show up as an realized short term loss, which it currently does not on my broker report (i believe because I had simply purchased the same equity in early December).  But again i believe that it should because the tax lot i relieved was over 30 days before the sale (october)