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Proof step 6 from proof maxScale-zero-01 (previous step)

(i / 10 ^ (maxScale(i / 10) + 1)) % 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 7:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 8:
0 ≤ maxScale(i / 10), (i / (10 ^ maxScale(i / 10) * 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-pot inst: name: succ seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [maxScale(i / 10), 10] flags: rewrite

Additional information

Used simplifier rules: maxScale-not-negt: ⊦ ¬ maxScale(i) < 0;%lels-01: ⊦ ¬ i ≤ j ↔ j < i; from specification int-abs Used terms: maxScale(i / 10), 10