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Proof step 4 from proof sorted-next-1 (previous step)

n % 2 = 1, x[2 + 2 * n0] < x[1 + 2 * n0], 2 * n0 < n, 2 + 2 * n0 < n → ¬ x[2 + 2 * n0] < x[1 + 2 * n0] ⊦ x[n + 1] < x[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n % 2 = 1, x[2 + 2 * n0] < x[1 + 2 * n0], 2 * n0 < n, n ≤ 2 + 2 * n0 ⊦ x[n + 1] < x[n]

Rule argument

Additional information

Used simplifier rules: mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ ¬ n < n; (s)% ⊦ m < n + 1 ↔ ¬ n < m; (s)% ⊦ m * n < m1 * n + n ↔ m < m1 + 1 ∧ n ≠ 0; (s)%fle: ⊦ m < n ∧ n ≤ n0 → m < n0; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)