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Proof step 12 from proof sublist-move (previous step)

m0 = m1 + 1, n + m ≤ 1 + # x0, m0 ≤ 1 + # x0, n + m ≤ m0, ∀ 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, a ' + firstn(m1, x0))) = firstn(m, restn(n, a ' + x0)), m0 = 0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 13:
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, a ' + firstn(m1, x0))) = firstn(m, restn(n, a ' + x0))

Rule argument

Additional information

Used simplifier rules: ⊦ m + n ≤ m + n0 ↔ n ≤ n0; (s)%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ m + 1 ≠ 0; (s)