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Theorem Inv-first-inner

⊦ Inv-first-inner(A, A0, x, y, i, j) ↔ # A ≠ 0 ∧ # A = # A0 ∧ i ≤ # A ∧ j ≤ i ∧ y ≤ x ∧ (j ≠ i → x < A[j + 2]) ∧ sorted(A, 0, j) ∧ sorted(A, j + 2, i + 2) ∧ (j ≠ i ∧ j ≠ 0 → A[j - 1] ≤ A[j + 2]) ∧ perm(A[j, y][j + 1, x], A0)