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Proof step 35 from proof bits2bytes-rec-02 (previous step)

n0 % 8 = 0, # bits = 16 + n0, ∀ bits0. # bits0 < (n0 + 8) + 8 → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ bits2bytes(restn(8, firstn(n0 + 8, bits))) = bits2bytes(firstn(n0, restn(8, bits))), bits = [], n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ m ≤ n ∧ m + n ≤ # bits → restn(m, firstn(n, bits)) = firstn(n - m, restn(m, bits))

Rule argument

seq: ⊦ m ≤ n ∧ m + n ≤ # bits → restn(m, firstn(n, bits)) = firstn(n - m, restn(m, bits)) subst: [bits, n, m] → [bits, n0 + 8, 8] rotate: F spec: list-del inst: bitlista name: restn-firstn

Additional information

Used simplifier rules: ⊦ 0 + m = m;% ⊦ n ≤ m → m + n0 - n = (m - n) + n0;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m + n = n + m;% ⊦ m < n ∧ m = n0 → n0 < n; (forward)% ⊦ m < n ∧ n = n0 → m < n0; (forward)% ⊦ m < n → ¬ n < m; Used terms: bits, n0 + 8, 8