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Proof step 10 from proof maxScale-zero-01 (previous step)

0 ≤ maxScale(i / 10), (i / (10 * 10 ^ maxScale(i / 10))) % 10 = 0, i % 10 = 0, ∀ i0. i→n(i0) < i→n(i) → (i0 / 10 ^ maxScale(i0)) % 10 = 0 → i0 = 0 ⊦ i = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 11:
⊦ j ≠ 0 ∧ j0 ≠ 0 → i / (j * j0) = (i / j) / j0
Proof step 12:
10 ≠ 0 ∧ 10 ^ maxScale(i / 10) ≠ 0, 0 ≤ maxScale(i / 10), ((i / 10) / 10 ^ maxScale(i / 10)) % 10 = 0, i % 10 = 0, ∀ i0. i→n(i0) < i→n(i) → (i0 / 10 ^ maxScale(i0)) % 10 = 0 → i0 = 0 ⊦ i = 0

Rule argument

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

Additional information

Used simplifier rules: maxScale-not-negt: ⊦ ¬ maxScale(i) < 0;%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot Used terms: 10 ^ maxScale(i / 10), 10, i