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Proof step 18 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), min(maxScale(i / 10), abs(j) - 1) < 0, ∀ 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 19:
⊦ ¬ j < i → min(j, i) = i
Proof step 20:
¬ ¬ maxScale(i / 10) < abs(j) - 1, i % 10 = 0, mkDecimal(i / 10, abs(j) - 1).int = (i / 10) / 10 ^ min(maxScale(i / 10), abs(j) - 1), min(maxScale(i / 10), abs(j) - 1) < 0, ∀ 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-min inst: name: Min-right seq: ⊦ ¬ j < i → min(j, i) = i subst: [i, j] → [abs(j) - 1, maxScale(i / 10)] flags: rewrite

Additional information

Used simplifier rules: abs-10: ⊦ abs(i) - 1 < 0 ↔ i = 0; from specification int-abs Used terms: abs(j) - 1, maxScale(i / 10)