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Proof step 3 from proof abs-any-def (previous step)

∀ i0, j. i→n(i0) < i→n(i) → true → abs(mkDecimal(i0, j)) = mkDecimal(abs(i0), j) ⊦ abs(mkDecimal(i, j)) = mkDecimal(abs(i), j)

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 → abs(mkDecimal(i0, j)) = mkDecimal(abs(i0), j) ⊦ abs(mkDecimal(i, j)) = mkDecimal(abs(i), j)
Proof step 16:
i % 10 = 0 ∧ j ≠ 0, ∀ i0, j. i→n(i0) < i→n(i) → true → abs(mkDecimal(i0, j)) = mkDecimal(abs(i0), j) ⊦ abs(mkDecimal(i / 10, abs(j) - 1)) = mkDecimal(abs(i), j)

Rule argument

spec: decimal 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

Additional information

Used terms: j, i