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Proof step 4 from proof sorted-next-0 (previous step)

n % 2 = 0, x[1 + 2 * n0] < x[2 * n0], 2 * n0 ≤ n, 1 + 2 * n0 < n → ¬ x[1 + 2 * n0] < x[2 * n0] ⊦ x[n + 1] < x[n]

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 5:
n % 2 = 0, x[1 + 2 * n0] < x[2 * n0], n ≤ 1 + 2 * n0, 2 * n0 ≤ n ⊦ x[n + 1] < x[n]

Rule argument

Additional information

Used simplifier rules: c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%mult-c: ⊦ m * n = n * m; from specification nat-mult%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult% ⊦ m ≤ m; (s)% ⊦ 2 * n ≤ 2 * m + 1 ↔ n ≤ m; (s)%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat% ⊦ m < n ↔ ¬ n ≤ m; (ss)