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Proof step 27 from proof bits2bytes-rec-02 (previous step)

n0 % 8 = 0, # bits = 16 + n0, bits2bytes(firstn(n0 + 8, bits)) = bits2bytes(firstn(8, firstn(n0 + 8, bits))) + bits2bytes(restn(8, firstn(n0 + 8, bits))), ∀ bits0. # bits0 < (n0 + 8) + 8 → true → # bits0 % 8 = 0 ∧ 8 < # bits0 → bits2bytes(bits0) = bits2bytes(firstn(8, bits0)) + bits2bytes(restn(8, bits0)) ⊦ bits2bytes(firstn(n0 + 8, bits)) + i2b(bits2int(lastn(8, bits))) ' = bits2bytes(firstn(8, bits)) + bits2bytes(firstn(n0, restn(8, bits))) + i2b(bits2int(lastn(8, restn(8, bits)))) ', bits = [], n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

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

Additional information

Used simplifier rules: ⊦ m + n = n + m;% ⊦ ¬ m ≤ n ↔ n < m;% ⊦ ¬ m + n < m;% ⊦ (m + n0) + n1 = m + n0 + n1;% ⊦ m = m0 + n0 ∧ n < n0 → ¬ m < m0 + n; Used terms: bits, n0 + 8, 8