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Proof step 67 from proof shiftright-rec-8-neg (previous step)

j0 * 128 >> (j - 1) = (j0 / 2 - 1) >> (j - 9), j0 % 2 = 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) ⊦ (j0 * 128) % 256 = 0, j = 8, j0 * 128 >> (j - 1) = j0 / 2 >> (j - 9), j = 0, j0 = 2 * (1 + j0 / 2)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 68:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)

Rule argument

seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [2, j0] rotate: F spec: int-div inst: name: modex

Additional information

Used simplifier rules: j % j0 = 0, j ≠ 0, j0 ≠ 0 ⊦ (i * (* j0)) / (* j) = i / j / j0;% ⊦ i / 1 = i;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;%i0 % j = 0, j ≠ 0 ⊦ (i * (* i0)) % (* j) = 0; Used terms: 2, j0