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• No-duplicatesp-equal
• Duplicity

No-duplicatesp-equal-same-by-duplicity

Proof strategy: show that a list satisfies no-duplicatesp-equal because it has no element whose duplicity is over 1.

This is often a good way to prove no-duplicatesp. This is a basic pick-a-point style theorem that you can (manually) functionally instantiate.

Definitions and Theorems

Theorem: duplicity-constraint

(defthm duplicity-constraint
  (implies (duplicity-hyp)
           (equal (duplicity a (duplicity-lhs))
                  (duplicity a (duplicity-rhs)))))

Theorem: no-duplicatesp-equal-same-by-duplicity

(defthm no-duplicatesp-equal-same-by-duplicity
  (implies (duplicity-hyp)
           (equal (no-duplicatesp-equal (duplicity-lhs))
                  (no-duplicatesp-equal (duplicity-rhs)))))

Subtopics

Duplicity-badguy

(duplicity-badguy x) finds an element that occurs multiple times in the list x, if one exists.