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Proof step 47 from proof int2bytes-len-neg-01 (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 48:
# int2bits(j) = m * 8 + n ∧ n < 8 ∧ 8 ≠ 0, j < 0, j + 2 ^ (8 * (i + 1) - 1) < 0, # int2bits(j) ≤ i→n(8 * (i + 1)) + 1, 0 ≤ i ⊦ j + 2 ^ (8 * (i + 1)) = 0, m + 1 = i→n(i + 2), n = 0

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