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Proof step 26 from proof int2bytes-first-neg (previous step)

int2bytes(i1 / 256) = by ' + bytes0, abs(i1 + 255) + i1 / 256 ≤ 0, i1 < 0, i1 < ~383, 0 ≤ b2i(by), ∀ bytes, by, i0. i→n(i0) < i→n(i1 + 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 27:
⊦ j < 0 → abs(j) = 0 - j
Proof step 28:
i1 + 255 < 0, int2bytes(i1 / 256) = by ' + bytes0, (0 - i1 + 255) + i1 / 256 ≤ 0, i1 < 0, i1 < ~383, 0 ≤ b2i(by), ∀ bytes, by, i0. i→n(i0) < i→n(i1 + 255) → int2bytes(i0) = by ' + bytes ∧ by ∈ int2bytes(i0) ∧ 0 ≤ b2i(by) ∧ i0 < 0 → false ⊦

Rule argument

seq: ⊦ j < 0 → abs(j) = 0 - j subst: [j] → [i1 + 255] rotate: F spec: int-abs inst: name: Abs-neg

Additional information

Used simplifier rules: ⊦ ¬ j < 0 → abs(j) = j;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;%j0 ≠ 0, j < j0 ⊦ i < (* j) → i < (* j0); Used terms: i1 + 255