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Proof step 11 from proof abs-any-def (previous step)

∀ i0, j. i→n(i0) < i→n(i) → true → abs(mkDecimal(i0, j)) = mkDecimal(abs(i0), j) ⊦ mkDecimal(abs(i), mkDecimal(i, j).scale) = mkDecimal(abs(i), j), i = 0, i % 10 = 0 ∧ j ≠ 0, j ≠ 0 ∧ i % 10 = 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).scale = abs(j)
Proof step 13:
¬(i % 10 = 0 ∧ j ≠ 0 ∧ i ≠ 0), ∀ i0, j. i→n(i0) < i→n(i) → true → abs(mkDecimal(i0, j)) = mkDecimal(abs(i0), j) ⊦ mkDecimal(abs(i), abs(j)) = mkDecimal(abs(i), j), i = 0, i % 10 = 0 ∧ j ≠ 0, j ≠ 0 ∧ i % 10 = 0

Rule argument

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

Additional information

Used terms: j, i