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Proof step 3 from proof mkDecimal-enlarge (previous step)

0 ≤ j0, ∀ j1, i, j. i→n(j1) < i→n(j0) → 0 ≤ j1 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j1, abs(j) + j1) ⊦ mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)

User applied rule insert rewrite lemma

And obtained the following new goals

Proof step 4:
⊦ 0 < i → j ^ i = j ^ i -1 * j
Proof step 5:
¬ 0 < j0, 0 ≤ j0, ∀ j1, i, j. i→n(j1) < i→n(j0) → 0 ≤ j1 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j1, abs(j) + j1) ⊦ mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0)
Proof step 8:
0 < j0, 0 ≤ j0, ∀ j1, i, j. i→n(j1) < i→n(j0) → 0 ≤ j1 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j1, abs(j) + j1) ⊦ mkDecimal(i, j) = mkDecimal(i * 10 ^ j0 -1 * 10, abs(j) + j0)

Rule argument

spec: int-pot inst: name: Pot-pos seq: ⊦ 0 < i → j ^ i = j ^ i -1 * j subst: [i, j] → [j0, 10] flags: rewrite

Additional information

Used terms: j0, 10