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Proof step 14 from proof ushort-pos-02 (previous step)

i % 65536 = 0, i < 0, i < ~32768, ~65536 < i ⊦ ~65536 = i

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 15:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)

Rule argument

seq: j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j) subst: [j, i] → [65536, i] rotate: F spec: int-div inst: name: modex

Additional information

Used simplifier rules: ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ 0 < i ∧ j < 0 → ((* i) * i0 < (* j) ↔ i0 < j / i);% ⊦ i < 0 ∧ 0 ≤ j → i < j;% ⊦ 0 < i ∧ j < 0 → ((* j) < (* i) * i0 ↔ (j + 1 - i) / i < i0);% ⊦ ~1 < i ↔ 0 ≤ i;% ⊦ i < j → (¬ ¬ j ≤ i ↔ false); Used terms: 65536, i