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Proof step 21 from proof int2bytes-rec-neg-05 (previous step)

# int2bits(j) % 8 = 0, # bits2bytes(int2bits(j)) = i→n(i) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + bits2bytes(int2bits(j)).rest

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
⊦ n ≠ 0 → (m % n = 0 ↔ (∃ n0. m = n0 * n))
Proof step 23:
8 ≠ 0, ∃ n0. # int2bits(j) = n0 * 8, # bits2bytes(int2bits(j)) = i→n(i) + 1, 0 < i, j + 2 ^ (i * 8 - 1) < 0, 0 < j + 2 ^ (i * 8), 0 < 2 ^ (i * 8) + j, j < 0 ⊦ j = 0, bits2bytes(int2bits(j)) = i2b(~1) ' + bits2bytes(int2bits(j)).rest

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)