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Proof step 23 from proof mkDecimal-selectors (previous step)

mkDecimal(i / 10, abs(i0) - 1) = mkDecimal(mkDecimal(i / 10, abs(i0) - 1).int, mkDecimal(i / 10, abs(i0) - 1).scale), i % 10 = 0, ∀ i1, i0. i→n(i1) < i→n(i) → true → mkDecimal(i1, i0) = mkDecimal(mkDecimal(i1, i0).int, mkDecimal(i1, i0).scale) ⊦ i0 = 0, i = 0, mkDecimal(i, i0).int = mkDecimal(i / 10, abs(i0) - 1).int ∧ mkDecimal(i, i0).scale = mkDecimal(i / 10, abs(i0) - 1).scale

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 24:
⊦ i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0 → mkDecimal(i, j).int = mkDecimal(i / 10, abs(j) - 1).int
Proof step 25:
i % 10 = 0 ∧ i0 ≠ 0 ∧ i ≠ 0, mkDecimal(i / 10, abs(i0) - 1) = mkDecimal(mkDecimal(i / 10, abs(i0) - 1).int, mkDecimal(i / 10, abs(i0) - 1).scale), i % 10 = 0, ∀ i1, i0. i→n(i1) < i→n(i) → true → mkDecimal(i1, i0) = mkDecimal(mkDecimal(i1, i0).int, mkDecimal(i1, i0).scale) ⊦ i0 = 0, i = 0, mkDecimal(i / 10, abs(i0) - 1).int = mkDecimal(i / 10, abs(i0) - 1).int ∧ mkDecimal(i, i0).scale = mkDecimal(i / 10, abs(i0) - 1).scale

Rule argument

spec: inst: name: intvalue-rec seq: ⊦ i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0 → mkDecimal(i, j).int = mkDecimal(i / 10, abs(j) - 1).int subst: [j, i] → [i0, i] flags: rewrite, current

Additional information

Used terms: i0, i