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Proof step 25 from proof sub-def-any (previous step)

∀ i1, i2, j, j0. i→n(i1) + i→n(i2) < i→n(i) + i→n(0) → true → mkDecimal(i1, j) - mkDecimal(i2, j0) = mkDecimal(i1 * 10 ^ abs(j0) - i2 * 10 ^ abs(j), abs(j) + abs(j0)) ⊦ j0 = 0, mkDecimal(i, j) = mkDecimal(i * 10 ^ abs(j0), abs(j) + abs(j0)), i % 10 = 0 ∧ j ≠ 0

User applied rule insert rewrite lemma

And obtained the following new goals

Rule argument

spec: decimal inst: name: mkDecimal-enlarge seq: ⊦ 0 ≤ j0 → mkDecimal(i, j) = mkDecimal(i * 10 ^ j0, abs(j) + j0) subst: [j0, j, i] → [abs(j0), j, i] flags: rewrite

Additional information

Used simplifier rules: abs-03: ⊦ 0 ≤ abs(i); from specification int-abs Used terms: abs(j0), j, i