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Proof step 32 from proof int2bytes-first-neg-01 (previous step)

int2bytes(i) = i2b(0) ' + bytes0, i * 256 < 255 * (i + 1), i * 256 + j < 0, 0 ≤ 255 * (i + 1) + j, i2b(0) ∈ int2bytes(i), abs(j) < 256, i * 256 + j < ~383, j ≤ 0, i ≤ 0, ∀ bytes, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = i2b(0) ' + bytes ∧ i0 < 0 ∧ i2b(0) ∈ int2bytes(i0) → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 33:
⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j
Proof step 34:
¬(255 * (i + 1) < 0 ∧ j < 0), int2bytes(i) = i2b(0) ' + bytes0, i * 256 < 255 * (i + 1), i * 256 + j < 0, 0 ≤ 255 * (i + 1) + j, i2b(0) ∈ int2bytes(i), abs(j) < 256, i * 256 + j < ~383, j ≤ 0, i ≤ 0, ∀ bytes, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = i2b(0) ' + bytes ∧ i0 < 0 ∧ i2b(0) ∈ int2bytes(i0) → false ⊦

Rule argument

seq: ⊦ i < 0 ∧ j < 0 → ¬ 0 ≤ i + j subst: [j, i] → [j, 255 * (i + 1)] rotate: F spec: int-abs inst: name: zero-ge-01

Additional information

Used terms: j, 255 * (i + 1)