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Proof step 17 from proof bits2bits-inj (previous step)

# bits % 8 = 0, # lastn(8, bits) = 8, 8 < # bits, ∀ bits0. # bits0 < # bits → # bits0 % 8 = 0 → bits0 = [] ∨ bytes2bits(bits2bytes(bits0)) = bits0 ⊦ (# bits - 8) % 8 = 0, bytes2bits(bits2bytes(firstn(# bits - 8, bits))) + lastn(8, bits) = bits, bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 18:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 19:
8 ≠ 0, ∃ n0. # bits = n0 * 8, # lastn(8, bits) = 8, 8 < # bits, ∀ bits0. # bits0 < # bits → # bits0 % 8 = 0 → bits0 = [] ∨ bytes2bits(bits2bytes(bits0)) = bits0 ⊦ (# bits - 8) % 8 = 0, bytes2bits(bits2bytes(firstn(# bits - 8, bits))) + lastn(8, bits) = bits, bits = []

Rule argument

seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [8, # bits] rotate: F spec: nat-div inst: name: modex

Additional information

Used terms: 8, # bits