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Proof step 121 from proof shiftright-rec-8-neg (previous step)

(i / 2 - 1) >> (j - 1) = ((i / 2 - 1) / 256 - 1) >> (j - 9), 8 < j, i < 0, 0 < j, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ i % 2 = 0, j = 0, (i / 2 - 1) >> (j - 1) = (i / 512 - 1) >> (j - 9), (i / 2 - 1) % 256 = 0, j = 8, i % 256 = 0, (i / 2 - 1) / 256 = i / 512

User applied rule insert elim lemma

And obtained the following new goals

Proof step 122:
i = i0 * 2 + j1 ∧ j1 ≤ 0 ∧ abs(j1) < 2 ∧ i0 ≤ 0 ∧ 0 < 2, (i0 - 1) >> (j - 1) = ((i0 - 1) / 256 - 1) >> (j - 9), 8 < j, i < 0, 0 < j, ∀ i, j0. i→n(j0) < i→n(j) → 8 ≤ j0 ∧ i < 0 ∧ 0 < j0 ∧ 0 ≤ j0 → i >> j0 = (i - 255) / 256 >> (j0 - 8) ⊦ j1 = 0, j = 0, (i0 - 1) >> (j - 1) = (i / 512 - 1) >> (j - 9), (i0 - 1) % 256 = 0, j = 8, i % 256 = 0, (i0 - 1) / 256 = i / 512

Rule argument

seq: ⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0) subst: [i, j, i0, j0] → [i, 2, i0, j1] rotate: T spec: int-div inst: name: div-elim-negpos

Additional information

Used simplifier rules: ⊦ ¬ i < j ↔ j ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false);%⊦ 0 < j ∧ i < 0 → ( i0 = i / j ∧ j0 = i % j ↔ i = i0 * j + j0 ∧ j0 ≤ 0 ∧ abs(j0) < j ∧ i0 ≤ 0); (elim) Used terms: i, 2, i0, j1