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Proof step 17 from proof mkDecimal-enlarge (previous step)

mkDecimal(i, j) = mkDecimal(i * 10 ^ (j0 - 1), abs(j) + j0 - 1), 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) ⊦ abs(j) + j0 = 0, mkDecimal(i, j) = mkDecimal(i * 10 ^ (j0 - 1), abs(abs(j) + j0) - 1)

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: int-abs inst: name: Abs-pos seq: ⊦ ¬ j < 0 → abs(j) = j subst: [j] → [abs(j) + j0] flags: rewrite

Additional information

Used simplifier rules: abs-08: ⊦ i < 0 → abs(i) = ~ i; from specification int-abs%subsub: ⊦ ~ i - j = ~(i + j); from specification int-abs%forward-lsle: ⊦ i < j ∧ j ≤ j0 → i < j0; (forward) from specification int-abs%forward-le-02: ⊦ j < i ∧ i ≤ 0 → j < 0; (forward) from specification int-abs%ls: ⊦ i + j < j ↔ i < 0; from specification int-basic2%absls: ⊦ ¬ abs(i) < 0; from specification int-abs%add-a: ⊦ i + j + i0 = (i + j) + i0; from specification int-basic2%add-c: ⊦ i + j = j + i; from specification int-basic2 Used terms: abs(j) + j0