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Proof step 13 from proof nodups-oc (previous step)

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

User applied rule cut formula

And obtained the following new goals

Proof step 6:
m0 ≤ n ∧ n < # A, nodups(A), m0 + 1 < # A, m0 < # A, ∀ A, n. nodups(A) ∧ m0 < # A → (n < m0 → #oc(A[n], A, m0) = 1) ∧ (m0 ≤ n ∧ n < # A → #oc(A[n], A, m0) = 0), n < m0 → #oc(A[n], A, m0) = 1, m0 ≤ n ∧ n < # A → #oc(A[n], A, m0) = 0 ⊦ (¬ m0 < n → #oc(A[n], A, m0) + (A[m0] = A[n] ⊃ 1;0) = 1) ∧ (m0 < n ∧ n < # A → #oc(A[n], A, m0) + (A[m0] = A[n] ⊃ 1;0) = 0)

Rule argument

fma:m0 ≤ n ∧ n < # A

Additional information

[Concretesimprules(()), Extrafmas((m0 ≤ n ∧ n < # A))]