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Proof step 33 from proof int2bytes-first-neg (previous step)

int2bytes(i) = by ' + bytes0, i ≤ 0, j ≤ 0, 0 ≤ b2i(by), i * 256 + j < ~383, abs(j) < 256, by ∈ int2bytes(i), 0 ≤ (i + 1) * 255 + j, i * 256 + j < 0, i * 256 < (i + 1) * 255, ∀ bytes, by, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = by ' + bytes ∧ by ∈ int2bytes(i0) ∧ 0 ≤ b2i(by) ∧ i0 < 0 → false ⊦

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 34:
⊦ i < 0 ∧ j0 < j ∧ 0 < j → ¬ 0 ≤ i * j + j0
Proof step 35:
¬(i + 1 < 0 ∧ j < 255 ∧ 0 < 255), int2bytes(i) = by ' + bytes0, i ≤ 0, j ≤ 0, 0 ≤ b2i(by), i * 256 + j < ~383, abs(j) < 256, by ∈ int2bytes(i), 0 ≤ (i + 1) * 255 + j, i * 256 + j < 0, i * 256 < (i + 1) * 255, ∀ bytes, by, i0. i→n(i0) < i→n((i * 256 + j) + 255) → int2bytes(i0) = by ' + bytes ∧ by ∈ int2bytes(i0) ∧ 0 ≤ b2i(by) ∧ i0 < 0 → false ⊦

Rule argument

seq: ⊦ i < 0 ∧ j0 < j ∧ 0 < j → ¬ 0 ≤ i * j + j0 subst: [j0, j, i] → [j, 255, i + 1] rotate: F spec: int-mult inst: name: modzero-03

Additional information

Used terms: j, 255, i + 1