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Proof step 105 from proof ushort-band-shift (previous step)

0 ≤ i0 * 256 + j0 + 255, abs(j0 - 1) < 256, abs(j0) < 256, ~65536 ≤ (i0 * 256 + j0) * 256 + j, ~256 < j, j < 0, ~256 ≤ j, ~255 ≤ i0 * 256 + j0, j0 ≤ 0, i0 * 256 + j0 < 0, (i0 * 256 + j0) * 256 + j < 0, i0 < 0 ⊦ i0 = ~1, j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ 0 ≤ j1 ∧ j1 < j → (0 ≤ i0 * j + j1 ↔ 0 ≤ i0) subst: [j1, j, i0] → [j0 + 255, 256, i0] rotate: F spec: int-mult inst: name: zero-ge-add

Additional information

Used simplifier rules: ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i ≤ 0 ∧ 0 ≤ j → i ≤ j;% ⊦ i * j = j * i;% ⊦ i + j = j + i;% ⊦ (* j) ≤ i0 + (* j0) ↔ j - j0 ≤ i0;%i0 ≠ 0, i0 ≤ i ⊦ (* i) ≤ j → (* i0) ≤ j;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ ¬ i ≤ j ↔ j < i;% ⊦ i + (* j) < (* j0) ↔ i < j0 - j;% ⊦ i < 1 ↔ i ≤ 0;% ⊦ i ≤ j → (¬ ¬ j < i ↔ false);% ⊦ i < (* j) ∧ j < 0 → i < 0; (forward)% ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ i < i + j ↔ 0 < j;% ⊦ 0 < i → (0 < i * j ↔ 0 < j);% ⊦ i < j → ¬ j < i;% ⊦ i * j * j0 = (i * j) * j0; Used terms: j0 + 255, 256, i0