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Proof step 37 from proof int2bytes-len-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 38:
⊦ i < ~1 ∧ 0 ≤ j → (0 ≤ 2 ^ j + i ↔ # int2bits(i) ≤ i→n(j) + 1)
Proof step 39:
¬(j < ~1 ∧ 0 ≤ 8 * (i + 1) - 1), 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1), 0 ≤ i, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, j < 0, 1 + i→n(i) * 8 < # int2bits(j) ⊦ j + 2 ^ (8 * i) = 0, # int2bits(j) / 8 = i→n(i), # int2bits(j) % 8 = 0
Proof step 42:
j < ~1 ∧ 0 ≤ 8 * (i + 1) - 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

Rule argument

seq: ⊦ i < ~1 ∧ 0 ≤ j → (0 ≤ 2 ^ j + i ↔ # int2bits(i) ≤ i→n(j) + 1) subst: [i, j] → [j, 8 * (i + 1) - 1] rotate: F spec: int2bits inst: name: int2bits-lslen-02

Additional information

Used terms: j, 8 * (i + 1) - 1