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Proof step 21 from proof sorted-next-1-swap (previous step)

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

Heuristic quantifier closing applied rule all left

And closed the goal!

Rule argument

pos: left 11 terms: n0

Additional information

Used simplifier rules: ⊦ m ≠ n → (m < n ↔ ¬ n < m); (ss)% ⊦ m < n → (n < m + 2 ↔ m + 1 = n); (s)%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic%c: ⊦ m + n = n + m; from specification nat-basic Used terms: n0