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Proof step 11 from proof equality-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → true → (mkDecimal(i1, j) = mkDecimal(i2, j0) ↔ i1 * 10 ^ abs(j0) = i2 * 10 ^ abs(j)) ⊦ mkDecimal(i, j).int = mkDecimal(i0, j0).int ∧ mkDecimal(i, j).scale = mkDecimal(i0, j0).scale ↔ i * 10 ^ abs(j0) = i0 * 10 ^ abs(j), i0 % 10 = 0 ∧ j0 ≠ 0, i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 12:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).int = i
Proof step 13:
¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0), ∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(i0) → true → (mkDecimal(i1, j) = mkDecimal(i2, j0) ↔ i1 * 10 ^ abs(j0) = i2 * 10 ^ abs(j)) ⊦ i = mkDecimal(i0, j0).int ∧ mkDecimal(i, j).scale = mkDecimal(i0, j0).scale ↔ i * 10 ^ abs(j0) = i0 * 10 ^ abs(j), i0 % 10 = 0 ∧ j0 ≠ 0, i % 10 = 0 ∧ j ≠ 0

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 terms: j, i