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Proof step 12 from proof mkDecimal-enlarge (previous step)

abs(j) + j0 = 0, 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, 0)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-basic2 inst: name: not-zero-pos seq: ⊦ 0 < i ∧ 0 < j → i + j ≠ 0 subst: [j, i] → [j0, abs(j)] flags: rewrite

Additional information

Used simplifier rules: abs-06: ⊦ 0 < abs(i) ↔ i ≠ 0; from specification int-abs%add-zero: ⊦ i + 0 = i; from specification int-basic2%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2%associativity: ⊦ i * j * j0 = (i * j) * j0; from specification int-mult%commutativity: ⊦ i * j = j * i; from specification int-mult%Mult-zero: ⊦ i * 0 = 0; from specification int-mult Used terms: j0, abs(j)