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Proof step 17 from proof int2bytes-len-pos-01 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 18:
# int2bits(j) = m * 8 + n ∧ n < 8 ∧ 8 ≠ 0, 0 ≤ i, j < 2 ^ (8 * (i + 1)), 2 ^ (8 * (i + 1) - 1) ≤ j ⊦ n = 0, m + 1 = i→n(i + 2)

Rule argument

seq: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n subst: [m, n, m0, n0] → [# int2bits(j), 8, m, n] rotate: T spec: nat-div inst: name: div-elim

Additional information

Used simplifier rules: n ≠ 0 ⊦ m0 = m / n ∧ n0 = m % n ↔ m = m0 * n + n0 ∧ n0 < n; (elim) Used terms: # int2bits(j), 8, m, n