| A[m] = A[i0], A[n] = A[i0], count(A[i0], mkbag(A, i0)) = 0, n < # A, m < # A, i0 < # A, n ≤ i0, m ≤ i0, 2 ≤ # A, ∀ A, n, m. A[n] = A[m] ∧ count(A[m], mkbag(A, i0)) = 1 ∧ m < # A ∧ n < # A ∧ m < i0 ∧ n < i0 ∧ 2 ≤ # A ∧ i0 ≤ # A → m = n ⊦ m = n |
A[n] = A[i0], A[m] = A[i0], count(A[i0], mkbag(A, i0)) = 0, i0 < # A, m < # A, n < # A, 2 ≤ # A, m ≤ i0, n ≤ i0 ⊦ m = n