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• Decoding-left-inverse

Encode-injective

Injectivity of encoding.

Different valid instructions are encoded differently. This is a direct consequence of decodex-of-encode: if two different instructions were encoded in the same way, the decoder would be unable to restore both at the same time.

Definitions and Theorems

Theorem: encode-injective

(defthm encode-injective
  (implies (and (instr-validp instr1 feat)
                (instr-validp instr2 feat))
           (equal (equal (encode instr1 feat)
                         (encode instr2 feat))
                  (equal (instr-fix instr1)
                         (instr-fix instr2)))))