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Proof step 10 from proof square-sqrt-02 (previous step)

dec.scale % 2 = 0, j * j = dec.int ⊦ mkDecimal(abs(j) * abs(j), 2 * abs(dec.scale) / 2) = dec

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
j ≠ 0 ⊦ i % j = 0 ↔ (∃ j0. i = j0 * j)
Proof step 12:
2 ≠ 0, ∃ j0. dec.scale = j0 * 2, j * j = dec.int ⊦ mkDecimal(abs(j) * abs(j), 2 * abs(dec.scale) / 2) = dec

Rule argument

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

Additional information

Used terms: 2, dec.scale