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Proof step 24 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)), 0 ≤ 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 25:
⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j
Proof step 26:
0 ≤ min(maxScale(i / 10), abs(j) - 1), i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = i / 10 ^ (min(maxScale(i / 10), abs(j) - 1) + 1), 0 ≤ 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-pot inst: name: succ seq: ⊦ 0 ≤ i → j ^ (i + 1) = j ^ i * j subst: [i, j] → [min(maxScale(i / 10), abs(j) - 1), 10] flags: rewrite

Additional information

Used simplifier rules: commutativity: ⊦ i * j = j * i; from specification int-mult Used terms: min(maxScale(i / 10), abs(j) - 1), 10