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Proof step 7 from proof int2bytes-len-neg (previous step)

# int2bits(j) % 8 = 0, # int2bits(j) % 8 = 0, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, j + 2 ^ (8 * i) ≤ 0 ⊦ # int2bits(j) / 8 = i→n(i) + 1

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 8:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 9:
8 ≠ 0, ∃ n0. # int2bits(j) = n0 * 8, ∃ n0. # int2bits(j) = n0 * 8, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, j + 2 ^ (8 * i) ≤ 0 ⊦ # int2bits(j) / 8 = i→n(i) + 1

Rule argument

seq: ⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n)) subst: [n, m] → [8, # int2bits(j)] rotate: F spec: nat-div inst: name: modex

Additional information

Used terms: 8, # int2bits(j)