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Proof step 24 from proof int2bytes-len-neg (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 25:
⊦ i < 0 ∧ 0 ≤ j ∧ ~ i ≠ 2 ^ j → (2 ^ j + i ≤ 0 ↔ ¬ # int2bits(i) ≤ i→n(j) + 1)
Proof step 26:
¬(j < 0 ∧ 0 ≤ 8 * i ∧ ~ j ≠ 2 ^ (8 * i)), j + 2 ^ (8 * i) ≤ 0, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, 0 ≤ i, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1) ⊦ # int2bits(j) % 8 = 0, # int2bits(j) / 8 = i→n(i)
Proof step 33:
j < 0 ∧ 0 ≤ 8 * i ∧ ~ j ≠ 2 ^ (8 * i), ¬ # int2bits(j) ≤ i→n(8 * i) + 1, 0 ≤ 2 ^ (8 * (i + 1) - 1) + j, 0 ≤ i, 2 ^ (8 * i) ≤ 2 ^ (8 * (i + 1) - 1) ⊦ # int2bits(j) % 8 = 0, # int2bits(j) / 8 = i→n(i)

Rule argument

seq: ⊦ i < 0 ∧ 0 ≤ j ∧ ~ i ≠ 2 ^ j → (2 ^ j + i ≤ 0 ↔ ¬ # int2bits(i) ≤ i→n(j) + 1) subst: [i, j] → [j, 8 * i] rotate: F spec: int2bits inst: name: int2bits-lelen-04

Additional information

Used simplifier rules: ⊦ i * j = j * i;% ⊦ i + j = j + i; Used terms: j, 8 * i