In a firm position
secure, fixed, stable, set, entrenched, settled, well-established, rooted, vested, officially recognized, old-line, deep-rooted, ingrained, unshakable; see also permanent 2, traditional 2.
Set up to endure
endowed, founded, organized, instituted, set up, realized, originated, chartered, incorporated, settled, inaugurated, codified, systematized, ratified, equipped, brought into existence, conceived, produced, begun, initiated, completed, finished.
Antonyms temporary*, unsound, insolvent.
Conclusively proved
verified, approved, guaranteed, endorsed, demonstrated, determined, confirmed, substantiated, accepted, assured, concluded, closed, authenticated, corroborated, found out, achieved, upheld, certain, ascertained, valid, validated, identified, proved, undeniable, sure, objectified.
Antonyms false*, invalidated, untrue.