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Proof step 12 from proof mkDecimal-maxScale-le (previous step)

maxScale(i) ≤ abs(j) ⊦ abs(j) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).scale + maxScale(i)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 13:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j)

Rule argument

spec: inst: name: scale-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j) subst: [j, i] → [abs(j) - maxScale(i), i / 10 ^ maxScale(i)] flags: rewrite, current

Additional information

Used simplifier rules: maxScale-zero-01: ⊦ (i / 10 ^ maxScale(i)) % 10 = 0 ↔ i = 0;%maxScale-zero: ⊦ maxScale(0) = 0;%abssub: ⊦ j ≤ i → abs(i - j) = i - j; from specification int-abs%Sub-def: ⊦ i + (j - i) = j; 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%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%lels-02: ⊦ i ≠ j → (i ≤ j ↔ i < j); from specification int-abs%abs-07: ⊦ abs(i) = 0 ↔ i = 0; from specification int-abs Used terms: abs(j) - maxScale(i), i / 10 ^ maxScale(i)