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Proof step 15 from proof mkDecimal-reduce-int (previous step)

i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = (i / 10) / 10 ^ min(maxScale(i / 10), abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(i) → true → mkDecimal(i0, j).int = i0 / 10 ^ min(maxScale(i0), abs(j)) ⊦ i = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ min(maxScale(i / 10) + 1, abs(j)), j = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 16:
⊦ j ≠ 0 ∧ j0 ≠ 0 → (i / j) / j0 = i / (j * j0)
Proof step 17:
¬(10 ≠ 0 ∧ 10 ^ min(maxScale(i / 10), abs(j) - 1) ≠ 0), i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = (i / 10) / 10 ^ min(maxScale(i / 10), abs(j) - 1), ∀ i0, j. i→n(i0) < i→n(i) → true → mkDecimal(i0, j).int = i0 / 10 ^ min(maxScale(i0), abs(j)) ⊦ i = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ min(maxScale(i / 10) + 1, abs(j)), j = 0
Proof step 23:
10 ≠ 0 ∧ 10 ^ min(maxScale(i / 10), abs(j) - 1) ≠ 0, i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = i / (10 * 10 ^ min(maxScale(i / 10), abs(j) - 1)), ∀ i0, j. i→n(i0) < i→n(i) → true → mkDecimal(i0, j).int = i0 / 10 ^ min(maxScale(i0), abs(j)) ⊦ i = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ min(maxScale(i / 10) + 1, abs(j)), j = 0

Rule argument

spec: int-div inst: name: div-div seq: ⊦ j ≠ 0 ∧ j0 ≠ 0 → (i / j) / j0 = i / (j * j0) subst: [j0, j, i] → [10 ^ min(maxScale(i / 10), abs(j) - 1), 10, i] flags: rewrite

Additional information

Used terms: 10 ^ min(maxScale(i / 10), abs(j) - 1), 10, i