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Proof step 244 from proof fix-bits2bytes-01 (previous step)

# bits % 8 = 0, # bits / 8 < n, bits.first ⊦ n * 8 = # bits, mklist(i2b(~1), n - # bits / 8) = bits2bytes(mklist(true, n * 8 - # bits)), bits = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 245:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 246:
8 ≠ 0, ∃ n0. # bits = n0 * 8, # bits / 8 < n, bits.first ⊦ n * 8 = # bits, mklist(i2b(~1), n - # bits / 8) = bits2bytes(mklist(true, n * 8 - # 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