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Proof step 35 from proof eq-same (previous step)

mkDecimal(i / 10, abs(j) - 1).scale = mkDecimal(mkDecimal(i / 10, abs(j) - 1).int, j).scale, i % 10 = 0, ∀ i1, i2, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(mkDecimal(i / 10, abs(j) - 1).int) → mkDecimal(i1, j0).scale = mkDecimal(i2, j0).scale ∧ mkDecimal(i1, j0).int = mkDecimal(i2, j0).int → i1 = i2 ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1).int % 10 = 0

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 36:
⊦ ¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0) → mkDecimal(i, j).scale = abs(j)
Proof step 37:
¬(mkDecimal(i / 10, abs(j) - 1).int % 10 = 0 ∧ j ≠ 0 ∧ mkDecimal(i / 10, abs(j) - 1).int ≠ 0), mkDecimal(i / 10, abs(j) - 1).scale = abs(j), i % 10 = 0, ∀ i1, i2, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(mkDecimal(i / 10, abs(j) - 1).int) → mkDecimal(i1, j0).scale = mkDecimal(i2, j0).scale ∧ mkDecimal(i1, j0).int = mkDecimal(i2, j0).int → i1 = i2 ⊦ j = 0, mkDecimal(i / 10, abs(j) - 1).int % 10 = 0

Rule argument

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

Additional information

Used terms: j, mkDecimal(i / 10, abs(j) - 1).int