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Proof step 21 from proof sublist-move (previous step)

n + m ≤ 1 + # x0, n + m ≤ m1 + 1, m1 ≤ # x0, ∀ n0, m0, n, m. n0 + m0 ≤ # x0 ∧ n + m ≤ m0 → firstn(m, restn(n, firstn(m0, restn(n0, x0)))) = firstn(m, restn(n0 + n, x0)) ⊦ firstn(m, restn(n - 1, firstn(m1, x0))) = firstn(m, restn(n, a ' + x0)), n = 0

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 22:
n = m2 + 1, m1 ≤ # x0, n + m ≤ m1 + 1, n + m ≤ 1 + # x0, ∀ n0, m0, n, m. n0 + m0 ≤ # x0 ∧ n + m ≤ m0 → firstn(m, restn(n, firstn(m0, restn(n0, x0)))) = firstn(m, restn(n0 + n, x0)) ⊦ firstn(m, restn(m2, firstn(m1, x0))) = firstn(m, restn(n, a ' + x0)), n = 0

Rule argument

spec: nat name: elim-pred-c seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m2]

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m2