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Proof step 19 from proof int2bytes-bytes2int-length-01 (previous step)

# sgn(bytes2bits(bytes)) % 8 = 0, # bytes < # sgn(bytes2bits(bytes)) / 8 ⊦ bytes = []

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 20:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 21:
8 ≠ 0, ∃ n0. # sgn(bytes2bits(bytes)) = n0 * 8, # bytes < # sgn(bytes2bits(bytes)) / 8 ⊦ bytes = []

Rule argument

spec: nat-div inst: name: modex seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [8, # sgn(bytes2bits(bytes))] flags: rewrite

Additional information

Used terms: 8, # sgn(bytes2bits(bytes))