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Proof step 14 from proof mkDecimal-maxScale-le-int (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [abs(j) - 1] flags: rewrite

Additional information

Used simplifier rules: sub-ls: ⊦ i - j < i0 ↔ i < j + i0; from specification int-abs%succ-02: ⊦ i < j + 1 ↔ i ≤ j; from specification int-abs%lels-03: ⊦ i < j → (¬ ¬ j ≤ i ↔ false); from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%abs-10: ⊦ abs(i) - 1 < 0 ↔ i = 0; from specification int-abs Used terms: abs(j) - 1