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Proof step 43 from proof int2bytes-len-neg (previous step)

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

User applied rule insert elim lemma

And obtained the following new goals

Proof step 44:
# int2bits(j) = m * 8 + n ∧ n < 8 ∧ 8 ≠ 0, i→n(i) * 8 < i→n(8 * (i + 1) - 1), j < ~1, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, # int2bits(j) ≤ i→n(8 * (i + 1) - 1) + 1, j < 0, 1 + i→n(i) * 8 < # int2bits(j) ⊦ j + 2 ^ (8 * i) = 0, m = i→n(i), n = 0, 8 * (i + 1) = 1

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