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Proof step 21 from proof ushort-band-shift (previous step)

s2i(sho) % 256 = 0, 0 ≤ (65536 + s2i(sho)) / 256, ~65536 ≤ s2i(sho), s2i(sho) < 0, ~256 < s2i(sho) ⊦ 0 = ((65536 + s2i(sho)) / 256) % 256

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 22:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)

Rule argument

seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [256, s2i(sho)] rotate: F spec: int-div inst: name: modex

Additional information

Used simplifier rules: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward)% ⊦ j < i ∧ i ≤ 0 → j < 0; (forward)% ⊦ i ≤ j ∧ 0 ≤ i → 0 ≤ j; (forward)% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i ∧ j < 0 → ((* j) < (* i) * i0 ↔ (j + 1 - i) / i < i0);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 256, s2i(sho)