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Proof step 7 from proof sublist-move (previous step)

n0 + 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, firstn(m0, restn(n0, a ' + x0)))) = firstn(m, restn(n0 + n, a ' + x0)), 0 < n0

Heuristic simplifier applied rule simplifier

And obtained the following new goals

Proof step 8:
n + m ≤ m0, m0 ≤ 1 + # x0, 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(n, firstn(m0, a ' + x0))) = firstn(m, restn(n, a ' + x0))

Rule argument

Additional information

Used simplifier rules: restN-zero: ⊦ restn(0, x) = x;%let: ⊦ n ≤ n0 ∧ n0 ≤ n1 → n ≤ n1; (forward) from specification nat%c: ⊦ m + n = n + m; from specification nat-basic%a: ⊦ (m + n0) + n1 = m + n0 + n1; from specification nat-basic% ⊦ 0 + m = m; (s)% ⊦ 0 < m ↔ m ≠ 0; (s)