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Proof step 9 from proof sorted-next-0-swap (previous step)

2 * n0 < # x, 2 * n0 + 1 < # x, x[2 * n0 + 1] < x[2 * n0], x[2 * n0] < x[2 * n0, x[2 * n0 + 1]][2 * n0 + 1, x[2 * n0]][2 * n0], x[2 * n0 + 1] < x[2 * n0, x[2 * n0 + 1]][2 * n0 + 1, x[2 * n0]][2 * n0], ∀ n. n < n0 → ¬ x[1 + 2 * n] < x[2 * n] ⊦ x = []

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: list-del name: put-at seq: m < # x ⊦ m ≠ n → x[m, a][n] = x[n] subst: [n, a, m, x] → [2 * n0, x[2 * n0], 2 * n0 + 1, x[2 * n0, x[2 * n0 + 1]]] flags: <all paths>

Additional information

Used simplifier rules: ⊦ 2 * m ≠ 2 * n + 1; (s)%mult-a: ⊦ m0 * m * n = (m0 * m) * n; from specification nat-mult%mult-c: ⊦ m * n = n * m; from specification nat-mult%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic% ⊦ n < # x → # x[n, a] = # x; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m < n → (n ≤ m ↔ false); (s)%m < # x ⊦ x[m, a][m] = a; (s)% ⊦ ¬ a < a; (s) Used terms: 2 * n0, x[2 * n0], 2 * n0 + 1, x[2 * n0, x[2 * n0 + 1]]