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Proof step 3 from proof getint-neg-02 (previous step)

∀ i0, j. i→n(i0) < i→n(i) → true → (mkDecimal(i0, j).int < 0 ↔ i0 < 0) ⊦ mkDecimal(i, j).int < 0 ↔ i < 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1)
Proof step 5:
¬(i % 10 = 0 ∧ j ≠ 0), ∀ i0, j. i→n(i0) < i→n(i) → true → (mkDecimal(i0, j).int < 0 ↔ i0 < 0) ⊦ mkDecimal(i, j).int < 0 ↔ i < 0
Proof step 8:
i % 10 = 0 ∧ j ≠ 0, ∀ i0, j. i→n(i0) < i→n(i) → true → (mkDecimal(i0, j).int < 0 ↔ i0 < 0) ⊦ mkDecimal(i / 10, abs(j) - 1).int < 0 ↔ i < 0

Rule argument

spec: inst: name: mkDecimal-rec seq: ⊦ i % 10 = 0 ∧ j ≠ 0 → mkDecimal(i, j) = mkDecimal(i / 10, abs(j) - 1) subst: [j, i] → [j, i] flags: rewrite, current

Additional information

Used terms: j, i