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Proof step 5 from proof int2bits-rec-neg-02 (previous step)

j % 2 = 0, j < 0 ⊦ j = ~1, j = 2 * (j - 1) / 2

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 6:
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, j] rotate: F spec: int-div inst: name: modex

Additional information

Used simplifier rules: ⊦ 2 * i ≠ ~1;% ⊦ i * j * j0 = (i * j) * j0;% ⊦ i * j = j * i;% ⊦ i ≠ 0 → (i * j = i * j0 ↔ j = j0);% ⊦ 0 < i → (i * j < 0 ↔ j < 0);% ⊦ j < 0 → (j * 2 - 1) / 2 = j; Used terms: 2, j