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Proof step 53 from proof shiftright-rec-8-neg (previous step)

(j0 * 256) / 2 >> (j - 1) = ((j0 * 256) / 2 - 255) / 256 >> (j - 9), ((j0 * 256) / 2) % 256 = 0, 8 < j, 0 < j, j0 < 0, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ j = 8, (j0 * 256) / 2 >> (j - 1) = (j0 - 1) / 2 >> (j - 9), j = 0, ((j0 * 256) / 2 - 255) / 256 = (j0 - 1) / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

seq: ⊦ i % 256 = 0 ∧ i < 0 → (i - 255) / 256 = i / 256 subst: [i] → [(j0 * 256) / 2] rotate: F spec: int-div inst: name: div-minus255-256-01

Additional information

Used simplifier rules: 0 < j ⊦ i / (* j) < 0 ↔ i + j ≤ 0;% ⊦ i + (* j) ≤ (* j0) ↔ i ≤ j0 - j;% ⊦ 0 < i ∧ j < 0 → ((* i) * i0 ≤ (* j) ↔ i0 ≤ (j + 1 - i) / i);% ⊦ i ≤ ~1 ↔ i < 0;% ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i + j + i0 = (i + j) + i0;% ⊦ i + j = j + i; Used terms: (j0 * 256) / 2