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From The Collaborative International Dictionary of English v.0.48:
established \established\ adj. 1. brought about or set up or accepted; especially long and widely accepted; as, distrust of established authority; a team established as a member of a major league; enjoyed his prestige as an established writer; an established precedent; the established Church. Contrasted with unestablished. [Narrower terms: entrenched; implanted, planted, rooted; official; recognized] [WordNet 1.5] 2. securely established; as, an established reputation. Syn: firm. [WordNet 1.5] 3. settled securely and unconditionally. Syn: accomplished, effected. [WordNet 1.5] 4. conforming with accepted standards. [WordNet 1.5] 5. shown to be valid beyond a reasonable doubt; as, the established facts in the case. Syn: proved. [WordNet 1.5 +PJC] 6. (Bot.) introduced from another region and persisting without cultivation; -- of plants. Syn: naturalized. [WordNet 1.5 +PJC]