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Proof step 5 from proof sorted-next-0 (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: nat name: anti seq: ⊦ m ≤ n → (n ≤ m ↔ m = n) subst: [m, n] → [1 + 2 * n0, n] flags: <all paths>

Additional information

Used simplifier rules: ⊦ (2 * m + 1) % 2 = 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% ⊦ m + 1 ≤ n ↔ m < n; (s)% ⊦ m < n ↔ ¬ n ≤ m; (ss)% ⊦ m ≤ n → (n ≤ m ↔ m = n); (s) Used terms: 1 + 2 * n0, n