Firmly established is a term that can be used to describe something that has been securely and permanently established. The crossword solutions for this term are STABLE (6 letters), DUGIN (5 letters), ROOTED (6 letters), ENROOTED (8 letters) and INVETERATE (10 letters). STABLE implies that something is secure and unchanging, while dugin suggests that it is deeply entrenched. ROOTED and enrooted both suggest that the thing is firmly planted and unlikely to move, while INVETERATE implies that it has been around for a long time and is unlikely to change.