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Proof step 12 from proof sorted-next-1-swap (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
m < # x ⊦ x[m, a][m] = a

Rule argument

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

Additional information

Used simplifier rules: ⊦ ¬ a < a; (s)%c: ⊦ m + n = n + m; from specification nat-basic Used terms: x[2 + 2 * n0], 2 * n0 + 1, x