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Proof step 6 from proof mkDecimal-maxScale-le-int (previous step)

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

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 7:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i

Rule argument

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

Additional information

Used simplifier rules: maxScale-not-negt: ⊦ ¬ maxScale(i) < 0;%maxScale-base: ⊦ i % 10 ≠ 0 ∧ i ≠ 0 → maxScale(i) = 0;%maxScale-le-zero: ⊦ maxScale(i) ≤ 0 ↔ maxScale(i) = 0;%pot-zero-01: ⊦ 0 < i → (i ^ j = 0 ↔ j < 0 ∧ 1 < i); from specification int-pot%div-eq-same-01: j ≠ 0 ⊦ i / j = i ↔ i = 0 ∨ j = 1; from specification int-div Used terms: j, i