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Proof step 14 from proof bits2bytes-rec-02 (previous step)

# bits = n0 * 8 + 8, n0 * 8 ≤ 8, ∀ bits0. # bits0 < # bits → 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(restn(8, bits)), bits = [], n0 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
⊦ n ≠ 0 → (m * n ≤ n ↔ m ≤ 1)
Proof step 16:
8 ≠ 0, # bits = n0 * 8 + 8, n0 ≤ 1, ∀ bits0. # bits0 < # bits → 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(restn(8, bits)), bits = [], n0 = 0

Rule argument

seq: ⊦ n ≠ 0 → (m * n ≤ n ↔ m ≤ 1) subst: [n, m] → [8, n0] rotate: F spec: nat-mult inst: name: leone

Additional information

Used terms: 8, n0