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Proof step 13 from proof int2bytes-len-pos (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 14:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 15:
8 ≠ 0, ∃ n0. # int2bits(j) = n0 * 8, 8 * i + 1 < 8 * (i + 1), # int2bits(j) ≤ i→n(8 * (i + 1) - 1) + 1, 0 ≤ i, i→n(8 * i) + 1 < # int2bits(j), 0 < j, 8 * i < abs(8 * (i + 1) - 1) ⊦ # 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)