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Proof step 5 from proof nodups-oc (previous step)

#oc(A[n], A, m0) = 0, m0 < # A, m0 + 1 < # A, nodups(A), n < # A, m0 ≤ n, ∀ A, n. nodups(A) ∧ m0 < # A → (n < m0 → #oc(A[n], A, m0) = 1) ∧ (m0 ≤ n ∧ n < # A → #oc(A[n], A, m0) = 0) ⊦ (¬ m0 < n → A[m0] = A[n]) ∧ (m0 < n → A[m0] ≠ A[n])

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 1:
⊦ nodups(A) ↔ (∀ m, m0. m ≠ m0 ∧ m < # A ∧ m0 < # A → A[m] ≠ A[m0])

Rule argument

spec: inst: name:nodups-def seq: ⊦ nodups(A) ↔ (∀ m, m0. m ≠ m0 ∧ m < # A ∧ m0 < # A → A[m] ≠ A[m0]) subst:[A] → [A] flags:rewrite, current

Additional information

[Concretesimprules(()), Extraterms((A))]