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Proof step 9 from proof mkDecimal-maxScale-le (previous step)

maxScale(i) ≤ abs(j) ⊦ i / 10 ^ maxScale(i) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).int ∧ 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 10:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i
Proof step 11:
¬((i / 10 ^ maxScale(i)) % 10 = 0 ∧ abs(j) - maxScale(i) ≠ 0 ∧ i / 10 ^ maxScale(i) ≠ 0), maxScale(i) ≤ abs(j) ⊦ i / 10 ^ maxScale(i) = i / 10 ^ maxScale(i) ∧ abs(j) = mkDecimal(i / 10 ^ maxScale(i), abs(j) - maxScale(i)).scale + maxScale(i)

Rule argument

spec: inst: name: intvalue-base seq: ⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i 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;%sub-eq: ⊦ i - j = i0 ↔ i = i0 + j; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + 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)